Slabs & Staircase

Q1. A rectangular slab panel has clear dimensions of 5.0 m × 4.0 m. It is continuous over three edges and discontinuous over one long edge, and it rests on beams 230 mm wide. The slab is subjected to an imposed load of 4 kN/m², a floor-finish load of 1.3 kN/m² and a probable partition-wall load of 1.5 kN/m². Include the self-weight of the slab. Design the slab, check shear, deflection and development length, and detail the reinforcement. Use Fe500 TMT steel and assume mild exposure conditions. [12] (2082 Bhadra, Q3b)

1. Panel classification and study assumptions. The concrete grade is not supplied; adopt M20 for this study calculation. Use the Table 26 condition one long edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe500 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1.3 and partition allowance 1.5 kN/m². The factored total is w_u = 17.700 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 188.05 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 36.949 kN/m; τ_v = 0.2111 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 566.41 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous long edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 127.32 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q2. A rectangular slab panel 5 m × 4 m (clear span) is continuous over three edges and discontinuous over one short edge, resting on a 230 mm wide beam, subjected to live load 5 kN/m² and floor finish 1.2 kN/m². Design the slab and check whether it satisfies the deflection criteria. Sketch the reinforcement at the support and midspan. Use M20 concrete and Fe415 steel. [13] (2081 Bhadra, Q3b)

1. Panel classification and study assumptions. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 5, finish load 1.2 and partition allowance 0 kN/m². The factored total is w_u = 16.800 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 161.56 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 35.070 kN/m; τ_v = 0.2004 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 131.79 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q3. Design a RC slab (interior panel) resting on RCC beams on all sides for a room of clear dimensions 4 m × 5 m, subjected to a superimposed live load of 3 kN/m² and floor finish 2 kN/m². Use M20 concrete and Fe415 steel. Perform necessary checks and provide structural drawings. [15] (2081 Baishakh, Q3a)

1. Panel classification and study assumptions. Beam width is not stated; assume 230 mm supports. Treat the interior panel as continuous on all edges. Use the Table 26 condition all four edges continuous (interior panel). Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 3, finish load 2 and partition allowance 0 kN/m². The factored total is w_u = 15.000 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 129.59 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 31.312 kN/m; τ_v = 0.1789 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner reinforcement: all adjoining edges are continuous, so no additional corner torsion mesh is required by the Annex D corner rule. Top support bars and edge-strip reinforcement are still necessary.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q4. Design a two-way slab for a room with clear dimensions of 6 m × 4 m. The slab is simply supported on all four edges by walls 230 mm thick and carries a superimposed working load of 4 kN/m². The corners of the slab are not held down. Use M25 concrete and Fe415 steel. [14] (2080 Bhadra, Q4b)

The question specifies a 6 m × 4 m clear slab on 230 mm walls, M25/Fe415, superimposed service load 4 kN/m², and corners not held down. Use Table 27. Adopt D = 200 mm and nominal cover 20 mm as study choices, with 10 mm short-span bars below 8 mm long-span bars. Thus d_x = 175 mm and d_y = 166 mm.

l_x = min(4.000 + 0.175, 4.230) = 4.175 m
l_y = min(6.000 + 0.166, 6.230) = 6.166 m
l_y/l_x = 1.47689
w_u = 1.5(0.200 × 25 + 4) = 13.50 kN/m²

For aspect ratios 1.4 and 1.5, Table 27 gives α_x = 0.099 and 0.104, and α_y = 0.051 and 0.046. Linear interpolation gives α_x = 0.102844 and α_y = 0.047156.

M_ux = 0.102844 × 13.50 × 4.175² = 24.20 kN·m/m
M_uy = 0.047156 × 13.50 × 4.175² = 11.10 kN·m/m

Solving M = 0.36f_ckbx_u(d − 0.42x_u) gives A_sx,required = 398.29 mm²/m and A_sy,required = 188.76 mm²/m. Minimum HYSD steel is 0.0012 × 1000 × 200 = 240 mm²/m.

A conservative full-load short-strip shear is V_u = 13.50 × 4.175/2 = 28.181 kN/m. Thus τ_v = 28181/(1000 × 175) = 0.161 MPa, below even a conservative 0.29 MPa concrete resistance for M25 without using the beneficial slab-depth factor. Main-bar spacing is below 300 mm and 3d, and the 10 mm diameter is below D/8 = 25 mm.

Remaining serviceability step: l_x/d_x = 23.857. The simply supported basic ratio 20 requires a tension modification factor of at least 1.193. Read the actual chart at the provided steel ratio and f_s = 0.58f_yA_s,required/A_s,provided before declaring the depth satisfactory. The flexure/shear checks above do not independently establish the long-term deflection result.

For the 10 mm Fe415 bars in M25, L_d = 10 × 361.05/(4 × 1.4 × 1.6) = approximately 403 mm. Check the support-anchorage provisions using the resistance of the bars continued and available end anchorage; do not assume that a 230 mm wall must contain the entire development length by itself. Corner hold-down torsion mesh is not required for this paper's explicitly unrestrained corners.

Q5. Design a reinforced concrete rectangular slab of size 4.0 m × 5.0 m to support an imposed load of 4 kN/m² and floor finish 1 kN/m². Two adjacent edges are discontinuous; slab rests on a 275 mm wide beam. Check the safety against shear and deflection. Use M20 concrete and Fe415 steel (torsional reinforcement not required). [12] (2080 Baishakh, Q3a)

1. Panel classification and study assumptions. Treat the stated panel dimensions as clear dimensions. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 275 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 15.000 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 181.15 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 31.312 kN/m; τ_v = 0.1789 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner reinforcement: the paper expressly excludes torsional-reinforcement design. The appropriate corner provision must still be considered in an actual restrained slab; do not change the specified edge condition merely because that part of the exam calculation is omitted.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q6. A rectangular slab panel 5 m × 4 m (clear span) is continuous over three edges and discontinuous over one short edge, resting on a 250 mm wide beam, subjected to live load 4 kN/m² and floor finish 1.5 kN/m². Design the slab and check deflection. Sketch the reinforcement at support and midspan with torsional bars. [10] (2079 Bhadra, Q2b)

1. Panel classification and study assumptions. Material grades are not supplied in this statement; assume M20 and Fe415. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 250 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1.5 and partition allowance 0 kN/m². The factored total is w_u = 15.750 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 151.26 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 32.878 kN/m; τ_v = 0.1879 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 123.39 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q7. Design a two-adjacent-sides-discontinuous RC slab for a room of clear dimensions 4 m × 4.5 m, resting on a 250 mm wide beam, with 25 mm thick PCC floor finish, live load 4.0 kN/m² and partition wall load 1.0 kN/m². Use M20 concrete and Fe415 steel. Check the slab for shear and deflection and show the reinforcement in plan and section along the short span. Design of torsional reinforcement in the slab is not required. [15] (2078 Bhadra, Q2b)

1. Panel classification and study assumptions. For the 25 mm PCC finish, assume unit weight 24 kN/m3, giving 0.60 kN/m2. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 250 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 4.665 m. The ratio is 1.11737, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 0.6 and partition allowance 1 kN/m². The factored total is w_u = 15.900 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 168.53 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 33.191 kN/m; τ_v = 0.1897 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner reinforcement: the paper expressly excludes torsional-reinforcement design. The appropriate corner provision must still be considered in an actual restrained slab; do not change the specified edge condition merely because that part of the exam calculation is omitted.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q8. Design a slab for a room of size 5 m × 4 m for a live load of 4 kN/m² and floor finish 1.2 kN/m². The slab is supported on 250 mm thick brick masonry walls with two adjacent edges discontinuous. Use M20 concrete and Fe415 bars. Carry out all checks, sketch the detailing plan and section, and the torsional reinforcement if required. [16] (2076 Ashwin, Q3)

1. Panel classification and study assumptions. Retain the stated two-edge discontinuity and assume the other edges develop the described continuity/hold-down. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 250 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1.2 and partition allowance 0 kN/m². The factored total is w_u = 15.300 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 184.87 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 31.939 kN/m; τ_v = 0.1825 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision where the two discontinuous edges meet, half provision at the two mixed-continuity corners, and none where both edges are continuous. Full provision is 0.75 times the area required for the largest positive midspan moment, or 150.80 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q9. Design a reinforced-concrete slab over a room of dimensions 5 m × 6 m. The slab is supported on masonry walls all around with adequate restraint, and its corners are held down. The live load is 3 kN/m², the floor-finish load is 1.5 kN/m² and the supporting walls are 230 mm thick. Use M20 concrete and Fe415 steel. Draw the top and bottom reinforcement arrangements in plan and section. Check the slab for deflection and development length. [14] (2076 Chaitra, Q5b)

1. Panel classification and study assumptions. Masonry support and corner hold-down do not prove flexural continuity; use the four-discontinuous-edge held-down case. Use the Table 26 condition all four edges discontinuous with corners held down. Adopt D = 225 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 200 mm and d_y = 190 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 5.200 m, l_y = 6.190 m. The ratio is 1.19038, confirming two-way action for four-side support.

3. Load. Self-weight = 25(225/1000) = 5.625 kN/m². Add live load 3, finish load 1.5 and partition allowance 0 kN/m². The factored total is w_u = 15.188 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 270.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 26.000. For the assumed simply supported basic ratio, the required modification-factor product is 1.300. For the short-span positive-moment steel, p_t = 0.2182% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 233.92 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 39.488 kN/m; τ_v = 0.1974 MPa. This is below the concrete resistance 0.3345 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision at all four held-down corners. Full provision is 0.75 times the area required for the largest positive midspan moment, or 318.03 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 150 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 1.040 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q10. Design a RCC slab for a room of clear dimensions 6 m × 4 m whose one short edge is discontinuous and corners are restrained, for a live load of 4 kN/m² and superimposed load 1.20 kN/m². Adopt M20 concrete and Fe415 steel. Check for deflection and development length. Give detailed sketches, section along short span, with torsional reinforcement. [16] (2075 Chaitra, Q4)

1. Panel classification and study assumptions. Support width is omitted; assume 230 mm. Treat the 1.20 kN/m2 superimposed load as additional to the stated live load. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 6.165 m. The ratio is 1.47665, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1.2 and partition allowance 0 kN/m². The factored total is w_u = 15.300 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 171.90 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 31.939 kN/m; τ_v = 0.1825 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 140.23 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q11. A rectangular slab panel 5 m × 4 m clear is continuous over three edges and discontinuous over one short edge. It carries floor finish 1.20 kN/m² and live load 4.0 kN/m² and rests on 225 mm wide beams. Design the slab panel and clearly sketch the top and bottom reinforcement. Use M20 concrete and Fe415 steel. [14] (2075 Ashwin, Q3a)

1. Panel classification and study assumptions. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 225 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 1.2 and partition allowance 0 kN/m². The factored total is w_u = 15.300 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 146.85 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 31.939 kN/m; τ_v = 0.1825 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 119.79 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q12. Design a restrained floor slab for a room 4 m × 5 m to support a live load of 5 kN/m², with two adjacent sides discontinuous. Use M20 concrete and Fe415 steel. Sketch the reinforcement details. [15] (2074 Chaitra, Q3b)

1. Panel classification and study assumptions. Assume 230 mm supports and a 1 kN/m2 finish because these are unspecified. Removing that finish changes the design loading. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 5, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 16.500 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 199.77 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 34.444 kN/m; τ_v = 0.1968 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision where the two discontinuous edges meet, half provision at the two mixed-continuity corners, and none where both edges are continuous. Full provision is 0.75 times the area required for the largest positive midspan moment, or 162.96 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q13. Design and detail an interior panel of a slab resting on RCC beams on all sides for a room of clear dimensions 4.5 m × 6.5 m, subjected to a superimposed live load of 4 kN/m² and floor finish 2.5 kN/m². Take M20 concrete and Fe415 steel. [15] (2073 Shrawan, Q2a)

1. Panel classification and study assumptions. Assume 230 mm support width. The panel is interior and continuous on all sides. Use the Table 26 condition all four edges continuous (interior panel). Adopt D = 225 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 200 mm and d_y = 190 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.700 m, l_y = 6.690 m. The ratio is 1.42340, confirming two-way action for four-side support.

3. Load. Self-weight = 25(225/1000) = 5.625 kN/m². Add live load 4, finish load 2.5 and partition allowance 0 kN/m². The factored total is w_u = 18.188 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 270.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.500. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.904. For the short-span positive-moment steel, p_t = 0.1354% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 199.90 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 42.741 kN/m; τ_v = 0.2137 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner reinforcement: all adjoining edges are continuous, so no additional corner torsion mesh is required by the Annex D corner rule. Top support bars and edge-strip reinforcement are still necessary.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q14. A rectangular slab panel 5.5 m × 4.0 m (clear span) is continuous over three edges and discontinuous over one short edge, resting on a 250 mm wide beam, subjected to live load 5 kN/m² and floor finish 1.0 kN/m². Design the slab, sketch the reinforcement at support and midspan separately with torsional bars, and check the deflection criteria. Checks for shear and development length are not necessary. [15] (2072 Chaitra, Q2a)

1. Panel classification and study assumptions. Assume M20 and Fe415 if the paper does not separately state material grades. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 250 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.665 m. The ratio is 1.35689, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 5, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 16.500 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 171.84 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

The paper expressly excludes shear and development-length checks. That examination exclusion does not remove these checks from an actual construction design.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 140.18 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q15. Design a slab for a room of size 3.6 m × 4.2 m at an intermediate storey of a residential building. The slab is prevented from lifting at its corners by supporting walls 230 mm thick. Take the live load as 3 kN/m² and the floor-finish load as 1 kN/m². Use M20 concrete and Fe415 steel. Carry out all necessary slab-design checks and sketch the reinforcement arrangement. [16] (2072 Kartik, Q2b)

1. Panel classification and study assumptions. Interpret the walls as providing corner hold-down without assuming rotational continuity into adjoining slabs. Use the Table 26 condition all four edges discontinuous with corners held down. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 3.775 m, l_y = 4.365 m. The ratio is 1.15629, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 3, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 13.500 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 21.571. For the assumed simply supported basic ratio, the required modification-factor product is 1.079. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 196.84 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 25.481 kN/m; τ_v = 0.1456 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision at all four held-down corners. Full provision is 0.75 times the area required for the largest positive midspan moment, or 160.57 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.755 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q16. Design a slab for a room of size 6.5 m × 4 m for a live load of 4.5 kN/m² and floor finish 1 kN/m², slab rigidly fixed with a 230 mm wide beam. Use M20 concrete and TMT bars. Draw top and bottom reinforcement detailing with sections and carry out all checks. [16] (2071 Chaitra, Q2b)

1. Panel classification and study assumptions. Interpret rigidly fixed edges as four continuous edges; assume Fe500 for the unspecified TMT grade. Use the Table 26 condition all four edges continuous (interior panel). Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe500 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 6.665 m. The ratio is 1.59641, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4.5, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 15.750 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 173.91 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 32.878 kN/m; τ_v = 0.1879 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 566.41 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner reinforcement: all adjoining edges are continuous, so no additional corner torsion mesh is required by the Annex D corner rule. Top support bars and edge-strip reinforcement are still necessary.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q17. The RC slab floor of a residential building is subjected to live load 3 kN/m² and floor finish 1 kN/m². Design panel 2 in the supplied floor plan for bending moment and shear force, and draw neat sketches showing top and bottom reinforcement. The plan consists of two 5 m bays horizontally and two 3 m bays vertically, enclosed by one-brick-thick walls; panel 2 is the upper-right panel. [14] (2069 Chaitra, Q3b)

1. Panel classification and study assumptions. Panel 2 in the supplied plan is a corner panel, with two exterior edges and two interior continuous edges. Assume a 230 mm one-brick wall convention and M20/Fe415, since the statement omits grades. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 175 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 150 mm and d_y = 140 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 3.150 m, l_y = 5.140 m. The ratio is 1.63175, confirming two-way action for four-side support.

3. Load. Self-weight = 25(175/1000) = 4.375 kN/m². Add live load 3, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 12.562 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 210.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 21.000. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.808. For the short-span positive-moment steel, p_t = 0.1745% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 128.85 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 19.786 kN/m; τ_v = 0.1319 MPa. This is below the concrete resistance 0.2996 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision where the two discontinuous edges meet, half provision at the two mixed-continuity corners, and none where both edges are continuous. Full provision is 0.75 times the area required for the largest positive midspan moment, or 105.11 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.630 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q18. Design a corner slab, with two adjacent edges discontinuous, of clear dimensions 5 m × 4 m to carry a live load of 3 kN/m² and floor finish of 1 kN/m². Use M20 concrete and Fe415 steel. Carry out all necessary checks and draw a neat sketch of the plan and section of the slab. [13] (2082 Baishakh, Q3b)

1. Panel classification and study assumptions. Assume 230 mm support width, which the statement does not supply. Use the Table 26 condition two adjacent edges discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 230 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 3, finish load 1 and partition allowance 0 kN/m². The factored total is w_u = 13.500 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 162.63 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 28.181 kN/m; τ_v = 0.1610 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply full provision where the two discontinuous edges meet, half provision at the two mixed-continuity corners, and none where both edges are continuous. Full provision is 0.75 times the area required for the largest positive midspan moment, or 132.67 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q19. Design a slab panel with one short edge discontinuous for a room of size 4 m × 5 m. The slab edges are supported on 250 mm wide walls. It carries a live load of 4 kN/m² and floor finish of 0.75 kN/m². Use M20 concrete and Fe415 steel. Sketch reinforcement detailing in plan and sections, and check deflection and development length. [15] (2074 Ashwin, Q2a)

1. Panel classification and study assumptions. Use the Table 26 condition one short edge discontinuous. Adopt D = 200 mm, nominal cover 20 mm and 10 mm bars in both directions. Place the short-span bottom bars below the long-span bars: d_x = 175 mm and d_y = 165 mm. Use M20 concrete and Fe415 steel.

2. Effective spans. With 250 mm supports, use the lesser of clear span plus directional effective depth and support centre spacing: l_x = 4.175 m, l_y = 5.165 m. The ratio is 1.23713, confirming two-way action for four-side support.

3. Load. Self-weight = 25(200/1000) = 5.000 kN/m². Add live load 4, finish load 0.75 and partition allowance 0 kN/m². The factored total is w_u = 14.625 kN/m².

4. Moments and reinforcement. Interpolate the short-direction coefficients at l_y/l_x in the selected Table 26 row. In both directions M = αw_ul_x² per metre width. Solve the rectangular section for steel using the correct directional depth; minimum HYSD area is 0.0012bD = 240.00 mm²/m.

Each selected spacing has been checked against its required area, 3d and 300 mm, and the provided section satisfies the flexural strain limit. In Table 26 design the maximum moments apply to the middle strips; provide minimum reinforcement in edge strips. A conservative uniform application of the scheduled steel over the whole panel is possible, but top bars still belong over the appropriate continuous edges.

5. Deflection check. l_x/d_x = 23.857. For the assumed continuous short-direction basic ratio, the required modification-factor product is 0.918. For the short-span positive-moment steel, p_t = 0.1496% and f_s = 0.58f_yA_{s,required in flexure}/A_s,provided = 140.25 MPa. Read the actual factor from the code chart, including any applicable qualifications, before declaring this depth satisfactory. No chart value is invented here.

6. Shear and anchorage. A conservative full-load short-strip support shear is w_ul_x/2 = 30.530 kN/m; τ_v = 0.1745 MPa. This is below the concrete resistance 0.2800 MPa without crediting the thin-slab enhancement. For 10 mm deformed bars, full-stress development length is 470.12 mm. Detail the available support anchorage using M₁/V + L_o and the applicable support-reaction allowance; do not assume the bearing width alone must contain the entire L_d.

Corner torsion mesh: apply half of the full corner provision at the two corners adjoining the discontinuous short edge; none at the other two. Full provision is 0.75 times the area required for the largest positive midspan moment, or 114.41 mm²/m in each of four layers: top and bottom, both directions. An 8 mm mesh at 300 mm centres satisfies this full requirement; half provision may use half that area, subject to spacing and other minimum steel. Extend the mesh at least l_x/5 = 0.835 m along both edges. Existing flexural bars may count only where correctly located, extended and anchored.

Detailing and conclusion. Show bottom steel, top support steel with code extension lengths, cover, directional bar layers and any required corner mesh in a plan and section. The schedule above establishes a trial flexural/shear arrangement under the stated assumptions. Final acceptance still requires the explicit deflection and support-anchorage checks described above.

Q1. Explain the concept of design of a staircase. Show the detailing of reinforcement of a straight flight in plan and section. [5] (2056 Bhadra, Q3a)

A longitudinally spanning stair carries load along its flight to the supporting landings, beams or walls. Its waist slab is designed as an inclined one-way slab, normally using a 1 m wide strip. The steps contribute dead load; their concrete is not automatically added to the effective structural waist thickness. A stair supported along its side edges has a different load path and must not be designed using the longitudinal-span model.

• Beams parallel to the risers at the top and bottom: identify the centre-to-centre distance between the actual supporting beams and apply the relevant span provision.
• Landings spanning in the same direction as the stair: analyse the flight and landings together between their supporting members; the flight's going alone is not the full structural span.
• Landings spanning transversely: the code's effective-span rule uses the going plus an allowance at each end of half the landing width or 1 m, whichever is smaller. This rule is not interchangeable with the previous two support cases.
• Loads (on plan, per metre width): self-weight of the waist (25×t·√(R²+T²)T for the slope), steps (½×25×R), finishes and LL (3–5 kN/m²). The landing carries a UDL over its length.
• Design: M = wl²8 (SS) → main bars along the span in the bottom of the waist; distribution steel across.

Here R is riser height, T is tread going and t is waist thickness measured normal to the inclined slab. The factor secθ = √(R² + T²)/T converts waist weight per slope area to weight per horizontal plan area. Do not apply it again after already converting the load. Use the occupancy-specific imposed load in the actual design, not an unqualified default.

Main bars follow the flight span and are anchored into the supporting member; distribution bars run across the width. Top bars are needed where the analysis gives negative moment over landings or supports. Provide chairs and spacers so the inclined bottom steel keeps its cover during concreting.

At a re-entrant flight/landing corner, a tension bar bent sharply around the corner tends to straighten and can break off the cover. Use a properly anchored crossing/lapping arrangement or a specifically designed confined bend rather than an unrestrained sharp tension bend. A plan should identify span direction, landing supports and bar marks; its matching longitudinal section should show the waist, steps, main bars, top support bars and anchorage.

Reference basis: slab coefficient cases and detailing were checked against the supplied Bhavikatti Chapter 7 and its reproduction of IS 456 Annex D. Example arithmetic has been recomputed; the source's OCR text is not used as an authority for unreadable table entries.

Q2. Draw the typical reinforcement drawing for a flight and a landing of an RCC staircase. Also define the effective span for a staircase. [5+1] (2074 Ashwin, Q4b)

A longitudinally spanning stair carries load along its flight to the supporting landings, beams or walls. Its waist slab is designed as an inclined one-way slab, normally using a 1 m wide strip. The steps contribute dead load; their concrete is not automatically added to the effective structural waist thickness. A stair supported along its side edges has a different load path and must not be designed using the longitudinal-span model.

• Beams parallel to the risers at the top and bottom: identify the centre-to-centre distance between the actual supporting beams and apply the relevant span provision.
• Landings spanning in the same direction as the stair: analyse the flight and landings together between their supporting members; the flight's going alone is not the full structural span.
• Landings spanning transversely: the code's effective-span rule uses the going plus an allowance at each end of half the landing width or 1 m, whichever is smaller. This rule is not interchangeable with the previous two support cases.
• Loads (on plan, per metre width): self-weight of the waist (25×t·√(R²+T²)T for the slope), steps (½×25×R), finishes and LL (3–5 kN/m²). The landing carries a UDL over its length.
• Design: M = wl²8 (SS) → main bars along the span in the bottom of the waist; distribution steel across.

Here R is riser height, T is tread going and t is waist thickness measured normal to the inclined slab. The factor secθ = √(R² + T²)/T converts waist weight per slope area to weight per horizontal plan area. Do not apply it again after already converting the load. Use the occupancy-specific imposed load in the actual design, not an unqualified default.

Main bars follow the flight span and are anchored into the supporting member; distribution bars run across the width. Top bars are needed where the analysis gives negative moment over landings or supports. Provide chairs and spacers so the inclined bottom steel keeps its cover during concreting.

At a re-entrant flight/landing corner, a tension bar bent sharply around the corner tends to straighten and can break off the cover. Use a properly anchored crossing/lapping arrangement or a specifically designed confined bend rather than an unrestrained sharp tension bend. A plan should identify span direction, landing supports and bar marks; its matching longitudinal section should show the waist, steps, main bars, top support bars and anchorage.

Reference basis: slab coefficient cases and detailing were checked against the supplied Bhavikatti Chapter 7 and its reproduction of IS 456 Annex D. Example arithmetic has been recomputed; the source's OCR text is not used as an authority for unreadable table entries.

Q3. Explain the detailing of reinforcement in staircases. [5] (2068 Baishakh, Q3a)

A longitudinally spanning stair carries load along its flight to the supporting landings, beams or walls. Its waist slab is designed as an inclined one-way slab, normally using a 1 m wide strip. The steps contribute dead load; their concrete is not automatically added to the effective structural waist thickness. A stair supported along its side edges has a different load path and must not be designed using the longitudinal-span model.

• Beams parallel to the risers at the top and bottom: identify the centre-to-centre distance between the actual supporting beams and apply the relevant span provision.
• Landings spanning in the same direction as the stair: analyse the flight and landings together between their supporting members; the flight's going alone is not the full structural span.
• Landings spanning transversely: the code's effective-span rule uses the going plus an allowance at each end of half the landing width or 1 m, whichever is smaller. This rule is not interchangeable with the previous two support cases.
• Loads (on plan, per metre width): self-weight of the waist (25×t·√(R²+T²)T for the slope), steps (½×25×R), finishes and LL (3–5 kN/m²). The landing carries a UDL over its length.
• Design: M = wl²8 (SS) → main bars along the span in the bottom of the waist; distribution steel across.

Here R is riser height, T is tread going and t is waist thickness measured normal to the inclined slab. The factor secθ = √(R² + T²)/T converts waist weight per slope area to weight per horizontal plan area. Do not apply it again after already converting the load. Use the occupancy-specific imposed load in the actual design, not an unqualified default.

Main bars follow the flight span and are anchored into the supporting member; distribution bars run across the width. Top bars are needed where the analysis gives negative moment over landings or supports. Provide chairs and spacers so the inclined bottom steel keeps its cover during concreting.

At a re-entrant flight/landing corner, a tension bar bent sharply around the corner tends to straighten and can break off the cover. Use a properly anchored crossing/lapping arrangement or a specifically designed confined bend rather than an unrestrained sharp tension bend. A plan should identify span direction, landing supports and bar marks; its matching longitudinal section should show the waist, steps, main bars, top support bars and anchorage.

Reference basis: slab coefficient cases and detailing were checked against the supplied Bhavikatti Chapter 7 and its reproduction of IS 456 Annex D. Example arithmetic has been recomputed; the source's OCR text is not used as an authority for unreadable table entries.