Reinforced Masonry

5.1  Basic Concept

5.1.1  Definition

The contrast with unreinforced masonry must be stated carefully, because it is the point of the definition:

5.1.2  Why masonry is reinforced

1. Masonry is strong in compression but almost useless in tension. Its flexural tensile strength is only 0.1–0.4 N/mm² and the permissible value is 0.07–0.14 N/mm² — roughly a hundredth of its compressive strength, and effectively zero in mud or weak lime mortar.
2. Earthquake and wind produce reversible tension in walls, both in-plane (at the heel of a shear wall) and out-of-plane (at mid-height of a wall spanning between floor and roof). Unreinforced masonry has no answer to this except mass and precompression.
3. Unreinforced masonry fails in a brittle manner once flexural or shear cracking starts, with very little warning and almost no energy dissipation — the very worst property in an earthquake.
4. The scope of URM is limited. It cannot economically produce tall walls, large openings, slender piers, retaining walls or tanks. Reinforcement removes those limits.
5. Reinforcement supplies ductility, which is what modern seismic codes actually reward: the response reduction factor R rises from about 1.5–2.25 for URM to 3.0–4.0 for reinforced masonry (see §5.5.6), which directly reduces the design earthquake force.

5.1.3  Forms of reinforced masonry — where the steel goes

5.1.4  Advantages of reinforced masonry

• Real flexural and shear capacity — walls can carry out-of-plane pressure and in-plane shear far beyond the cracking load.
• Genuine ductility and energy dissipation; the failure is preceded by visible cracking, giving warning.
• Better out-of-plane performance, which is what actually kills people in masonry buildings.
• Taller walls, thinner walls, larger openings and higher slenderness ratios become possible.
• Higher R value in seismic design → lower design base shear.
• Uses the same materials and trades as ordinary masonry — no expensive plant, unlike RC frames.
• Cracks are distributed and fine rather than few and wide, which improves both repairability and durability.

5.1.5  Applications

Shear walls; load-bearing walls of multi-storey buildings; retaining walls; water tanks and reservoirs; footbridges; reinforced masonry columns, beams and lintels; seismic bands and vertical reinforcement at corners and openings; and, as a strengthening measure, jacketing of existing unreinforced walls. Prestressed (post-tensioned) masonry is the further step, in which vertical tendons apply artificial precompression so that tension never develops at all.

5.1.6  Materials and permissible stresses

Design follows the working stress (permissible stress) method, with stresses computed on a transformed section using the modular ratio, and stiffness computed on the uncracked section for analysis purposes.

Size, spacing, cover and anchorage — the detailing rules

Standard hooks may be used to make up any deficiency in development length: a 180° turn plus an extension of at least 4 bar diameters (minimum 64 mm); a 90° turn plus an extension of at least 12 bar diameters; and for stirrups and ties only, a 90° or 135° turn plus an extension of at least 5 bar diameters.

5.2  Vertical and Horizontal One-Way Flexural Behaviour

A wall loaded normal to its plane — by wind, by earth pressure, or by its own out-of-plane inertia in an earthquake — behaves as a slab. If it is supported on only two opposite edges it spans one way, and the direction of that span decides everything about how it must be reinforced.

5.2.1  The two one-way cases

5.2.2  Design moments for the one-way strip

Take a strip of unit width and analyse it as a beam. The coefficient depends entirely on the edge restraint, and stating it is worth marks:

The out-of-plane pressure itself is w = the wind pressure, or for earthquake w = A_h × (weight of wall per unit area) = A_h γ t.

5.2.3  Effective span and effective compressive width

The effective span of a one-way member is taken as the lesser of the centre-to-centre distance between supports and the clear span plus the effective depth.

This is the reinforced-masonry equivalent of the effective flange width of a T-beam: it stops the designer from assuming that one bar can mobilise the whole wall.

5.3  Two-Way Flexural Behaviour

A wall panel supported on three or four edges — by the floor, the roof and one or two cross walls — does not span one way. It bends about both axes at once, and the load finds its way to the supports along the stiffest and strongest path. Because the horizontal direction is roughly twice as strong, a two-way panel sheds a disproportionate share of the load sideways.

5.3.1  Why two-way action matters

• The design moment falls dramatically — often to a third or a quarter of the equivalent one-way value — simply because the panel is supported on more edges.
• It is the reason cross walls, piers and buttresses are so effective: adding a vertical support converts a weak one-way vertical span into a strong two-way panel.
• It explains the observed crack patterns in earthquakes: a two-way panel cracks along diagonal “yield lines” running from the corners, plus a horizontal crack at mid-height and a vertical crack at mid-span — not the single clean horizontal crack of a one-way wall.

5.3.2  Analysis by the yield-line (fracture-line) method

Masonry has no plastic plateau, so the lines are properly called fracture lines, but the algebra is the same as for a concrete slab. The design moment per unit width is written with a coefficient:

5.3.3  Design consequences

1. Reinforce in both directions — vertical bars for the vertical span, bed-joint reinforcement or bond beams for the horizontal span.
2. The corners attract the largest moments and are where the fracture lines start, so corner reinforcement and proper interlocking of the return walls are essential.
3. Two-way action only develops if the edges are genuinely restrained — the wall must be properly tied to the diaphragm and bonded into the cross walls. An unanchored wall reverts to a one-way cantilever with five times the moment.
4. Because it is stronger, two-way action allows thinner walls and larger panels for the same pressure.

5.4  Flexural and Shear Strength

5.4.1  Flexural strength — working stress design of a reinforced section

The section is analysed exactly like a singly reinforced concrete beam, using the cracked transformed section: the masonry below the neutral axis is ignored, and the steel area is transformed by the modular ratio n = E_s/E_m.

Where F_b is the permissible bending compressive stress in the masonry (commonly taken as f_m/4 for reinforced brickwork) and F_s is the permissible steel stress from §5.1.6. The section should be kept under-reinforced, so that the steel reaches its permissible stress first and the failure is ductile.

5.4.2  Permissible compressive force

The coefficient 0.25 gives a factor of safety of about 4.0 against crushing of the masonry; the coefficient 0.65 on the steel term was determined from tests. Note that both the masonry and the steel contribute in compression — unlike shear, where they are not added.

5.4.3  Shear strength

If there is tension in any part of a section, that area must be ignored when working out the shear stress — a cracked zone cannot be relied on to carry shear.

Permissible shear stress F_v — flexural members

Permissible shear stress F_v — walls

For walls the permissible shear depends on the aspect ratio, expressed as M/Vd — the ratio of moment to shear times depth, which is essentially the height-to-length ratio of the wall:

In a cantilever beam the maximum shear at the support must be used. For a member under a uniformly distributed load, the maximum shear may be taken at 0.5d from the face of the support, provided the support reaction causes compression in the end region and there is no concentrated load within that distance.

5.4.4  Behaviour and failure mechanisms of reinforced masonry shear walls

The behaviour under combined shear, axial load and moment depends on the level of axial compression, the amount of horizontal and vertical reinforcement, the wall aspect ratio, and the material properties. There are two families of failure, each with sub-modes (FEMA 306):

5.5  Reinforced Masonry Column, Beam and Bands

5.5.1  General

A reinforced masonry column is an isolated vertical compression member whose width does not exceed 4 times its thickness; anything longer is a wall. A beam in masonry is usually a lintel spanning an opening. A band is a horizontal reinforced beam cast within the thickness of the wall and running continuously around the whole building.

5.5.2  Reinforced masonry columns

Why ties matter: they provide lateral support to the longitudinal bars to prevent them buckling (the critical unsupported length is about 16 bar diameters), and they resist diagonal tension when the column acts in shear. They may be placed in the mortar joints.

5.5.3  Reinforced masonry beams — the reinforced brick lintel

This is the element the exam actually asks you to design. The full worked solutions are on the solved-paper pages; here is the method.

1. Decide whether arching action develops. If the wall on either side of the opening extends beyond the springing by at least half the span, and the masonry above the lintel is at least as deep as the load triangle, the masonry arches over the opening and the lintel carries only the 45° triangle of masonry (height L/2). Otherwise it carries the full rectangle of masonry above it, plus any floor or roof load landing in that zone.
2. Compute the load. Triangle: W = ½ × L × (L/2) × t × γ. Add the self weight of the lintel as a UDL.
3. Compute the moment and shear. For a triangular load of total magnitude W on a simply supported span L: M = WL/6 and V = W/2. For the UDL self weight: M = wL²/8, V = wL/2.
4. Set the working-stress constants. σ_cbc = f_m/4; σ_st = 230 MPa for Fe 415; m = 280/(3σ_cbc); k = mσ_cbc/(mσ_cbc + σ_st); j = 1 − k/3; R = ½σ_cbckj.
5. Find the required depth d = √(M/Rb) and provide an overall depth in whole brick courses (typically three courses ≈ 230 mm), then compute the effective depth d = D − cover − φ/2.
6. Find the steel A_st = M/(σ_st j d). This is almost always far below the practical minimum, so provide 2 bars of 10–12 mm laid in the vertical joints of the bottom course and fully grouted with 1:3 cement mortar.
7. Check shear τ_v = V/(bjd) against about 0.10 N/mm² for reinforced brickwork, and provide nominal 6 mm links at 150 mm centres to hold the bars.
8. Check bearing and anchorage. Minimum bearing 200 mm each end; the bars run the full length with a 90° hook, giving anchorage well beyond L_d = 0.25 d_bF_s.

5.5.4  Seismic bands

A band is a horizontal reinforced beam cast within the wall thickness and running continuously around the entire building at one level. Bands are the single most cost-effective seismic measure available for masonry construction — in the 2015 Gorkha earthquake, buildings with even one lintel band frequently survived with repairable damage while identical unbanded neighbours collapsed.

The six bands and what each does

How a band is loaded — biaxial bending

Detailing rules — IS 4326 cl. 8.4 / NBC 202

• Minimum band depth 75 mm, full thickness of the wall, concrete not leaner than M15.
• Minimum 2 longitudinal bars of 8 mm φ with 6 mm φ links at 150 mm centres. For longer spans and higher seismic zones the bars increase to 12 or 16 mm.
• The band must be continuous around the whole building and at the same level all round — it must never be interrupted at a door or window.
• At every corner and T-junction, provide L-shaped bars of the same diameter lapped 60φ.
• The lintel band may be combined with the roof band if the two are within 300 mm of each other.
• Bands must be combined with vertical reinforcement at all corners, T-junctions and the jambs of large openings — horizontal bands alone cannot resist out-of-plane overturning.

5.5.5  Minimum reinforcement for seismic performance

5.5.6  The three wall types and their R values

5.5.7  Detailing of reinforced masonry shear walls

• Wall thickness preferably not less than 150 mm.
• Bar diameter ≤ one-tenth of the wall thickness; bar spacing in either direction limited so the reinforcement is well distributed.
• The effective flange width of a flanged wall is restricted to the lesser of half the distance to an adjacent web and a fraction of the total wall height.
• Vertical reinforcement comprises both distributed reinforcement and concentrated reinforcement near each end.
• A minimum of 4 nos 12 mm bars in at least two layers near each end of the wall.
• Where the extreme-fibre compressive stress exceeds 0.2 f_ck, boundary elements must be provided along the vertical edges — a locally thickened, heavily tied zone that confines the compression toe and prevents the crushing and out-of-plane instability described in §5.4.4.

Quick Revision

Chapter Summary

1. §5.1 — Basic concept. Reinforced masonry is masonry designed on the assumption that flexural tension is carried by reinforcement only. It exists because masonry has essentially no tensile strength and fails in a brittle way. The steel can be placed in grouted hollow cores, in pockets, in Quetta-bond cavities, in filled cavity walls, in beam units, or in the bed joints. The reward is flexural and shear capacity, ductility, better out-of-plane behaviour and a higher R factor. Design is by working stress with permissible steel stresses of 230/190 MPa (HYSD) and 140-130/130 MPa (MS), and L_d = 0.25 d_bF_s ≥ 300 mm.
2. §5.2 — One-way flexure. A wall spanning vertically cracks along a bed joint and is weak (0.07 N/mm²), and needs vertical bars; a wall spanning horizontally must break through the units and is about twice as strong (0.14 N/mm²), and needs bed-joint reinforcement. The moment coefficient depends on the restraint: wH²/8, /10, /12, or /2 for a free top. Effective compressive width per bar is limited to 3t (also ≤ the bar spacing and ≤ 6t).
3. §5.3 — Two-way flexure. A panel supported on three or four edges spans both ways and its design moment falls to a fraction of the one-way value: M = αwL², with α taken from code tables as a function of the edge conditions, the aspect ratio and the orthogonal strength ratio. This is precisely why cross walls, piers and buttresses are so effective, and it produces the diagonal fracture-line crack patterns seen after earthquakes.
4. §5.4 — Flexural and shear strength. Flexure uses the cracked transformed section with k, j and R exactly as in RC. Compression uses P_o = (0.25 f_mA_n + 0.65 A_stF_s)k_s, with combined stress limited to 1.25 F_a. In shear the crucial rule is that masonry and steel contributions are not added — if f_v exceeds F_v, the steel must carry the whole shear. The permissible shear rises sharply for squat walls (low M/Vd). Failure is either flexural (ductile yielding, lap splice slip, out-of-plane instability) or shear (diagonal tension, sliding shear); the ductile flexural mode with a plastic hinge at the base is the one the design must deliberately produce.
5. §5.5 — Columns, beams and bands. Columns take 0.25–4% vertical steel with at least 4 bars and ties at the least of 16d_b, 48d_tie and the least dimension. Reinforced brick lintels are designed for the 45° arching triangle with M = WL/6, and in practice come out governed by detailing rather than strength. Bands — plinth, sill, lintel, floor, roof and gable — are horizontal beams cast in the wall, bent about two axes at once, and must be continuous all round with 60φ corner laps; they are the cheapest and most effective seismic measure in masonry. Minimum seismic steel is 100 mm² at corners, beside openings and at wall ends at 3 m maximum spacing, and the three wall types A, B and C earn R = 2.25, 3.0 and 4.0 respectively.

All Past Questions on This Chapter

Chapter 5 — Reinforced Masonry · 5 hours · 6 marks · ENCE 367 Seismic Resistant Design of Masonry Structures