Paper Information
| Detail | Information |
|---|---|
| Exam | 2078 Bhadra |
| Subject | Seismic Resistant Design of Masonry Structure (Elective I) — CE 72502 |
| Full Marks · Pass Marks · Time | 80 · 32 · 3 hours |
| Instructions | Attempt All questions. Necessary codes are allowed. Assume suitable data if necessary. |
Question 1
Richter scale — a MAGNITUDE scale
- Devised by Charles F. Richter in 1935. It is a quantitative, instrumental measure of the size of an earthquake — of the total energy released at the source.
- Based on the logarithm (base 10) of the maximum trace amplitude recorded by a standard Wood–Anderson seismograph, corrected to a standard epicentral distance of 100 km: ML = log10A − log10A0.
- Because it is logarithmic, one unit of magnitude = 10× the wave amplitude and about 31.6 (≈32)× the energy. M7.7 releases ~31× the energy of M6.7 and ~1000× that of M5.7.
- Energy relation: log10E = 11.8 + 1.5 M (E in ergs).
- One value per earthquake, independent of the observer's position and of the local soil or buildings. Expressed in Arabic numerals with a decimal.
- Open-ended and can be negative, but it saturates above about M7 — which is why the non-saturating moment magnitude Mw is now used for large events.
- Classification: <3 micro/minor, 3–3.9 minor, 4–4.9 light, 5–5.9 moderate, 6–6.9 strong, 7–7.9 major, ≥8 great.
MMI scale — an INTENSITY scale
- The Modified Mercalli Intensity scale is a qualitative, observational measure of the effects of an earthquake at a particular place — on people, objects, buildings and the ground.
- It has 12 grades written in Roman numerals, I to XII. No instrument is used; the grade is assigned from damage surveys and human reports.
- Many values per earthquake — a different value at every location. It is highest near the epicentre and decreases outward.
- Lines joining points of equal intensity are isoseismals; their map is used to locate the epicentre of historic (pre-instrumental) earthquakes and to prepare seismic hazard maps.
- It depends on epicentral distance, the local soil, and the type and quality of the buildings.
- Key grades: VII considerable damage in poorly built masonry; VIII partial collapse of ordinary masonry; X most masonry destroyed with its foundations; XII total damage.
- Other intensity scales: MSK-64 (also 12 grades, used in Europe and India) and the JMA scale (Japan).
Close with the one-line contrast: the Richter scale measures how big the earthquake was; the MMI scale measures how badly it shook a particular place.
The 2015 Gorkha earthquake (Mw 7.8, 25 April 2015, epicentre Barpak, focal depth ~15 km, followed by an Mw 7.3 aftershock on 12 May) damaged or destroyed about 800,000 buildings, the great majority of them unreinforced masonry. The major failure mechanisms observed were:
- Out-of-plane collapse of walls — by far the dominant mechanism, caused by unanchored flexible timber floors and roofs, the absence of bands, and slender walls in the upper storeys.
- Corner separation and vertical cracking at wall junctions, from poor interlocking of the courses at the corners.
- Delamination and collapse of multi-wythe walls — both burnt-brick-in-cement and un-coursed random rubble walls with CGI roofs, because through-stones were missing.
- In-plane diagonal (X) shear cracking of piers between openings, and vertical cracking at the corners of openings.
- Failure of gable walls, pulling down the top of the end walls and the roof.
- Separation of the roof from the walls, followed by collapse of heavy tiled roofs on the occupants.
- Soft / open ground storey failure in shop-front buildings, and short-column failures created by mezzanines.
- Total collapse of unreinforced stone-in-mud houses in the rural districts around the epicentre.
- Widespread failure of temples, monuments and monasteries, several already weakened by earlier earthquakes; plus lifeline failures (e.g. collapse of a penstock in Sindhupalchowk).
Sketch to draw
One isometric of a simple masonry building marked with: separation of walls at corners, diagonal (X) cracking in the in-plane wall, out-of-plane overturning of the transverse wall, separation of the roof from the walls, vertical cracking at openings and gable collapse.
Question 2
| Type | Advantages | Disadvantages |
|---|---|---|
| Brick masonry (burnt clay units) |
Uniform shape and size → good bond and thin joints; good strength (3.5–35 N/mm²); easy to form openings and bands; durable, fire and weather resistant; locally manufactured. | Needs good clay, fuel and kilns (energy and pollution); quality varies between kilns; heavy; weak in tension. |
| Stone masonry (random rubble, coursed rubble, squared, ashlar) |
Very high unit strength; extremely durable; locally available free of cost in hill areas; attractive; good thermal mass. | Irregular shapes give poor bond and very thick joints; walls are multi-leaf and delaminate; very heavy; needs skilled masons; the worst-performing type in Nepali earthquakes. |
| Concrete block masonry | Accurate dimensions, fast construction (large units), fewer joints, uniform quality, can be reinforced through the hollow cores. | Needs cement and a plant; drying shrinkage cracking; higher initial cost. |
| Adobe / earthen masonry | Cheapest; zero-energy production; excellent thermal comfort; entirely local material and skills. | Very low strength, no tensile capacity, degrades on wetting, erodes; extremely vulnerable in earthquakes (NBC 204). |
| Composite / faced masonry | Combines an economical backing (rubble, block) with a good-quality facing (brick, ashlar). | The two leaves have different stiffness and separate unless properly bonded through with headers. |
Add the general advantages of masonry (high compressive strength, durability, low-cost local materials, no complicated plant, fire and thermal performance, design flexibility, life > 500 years in lime mortar) and its general disadvantages (negligible tensile strength, heavy so large foundations and large inertia forces, brittle, frost and sulphate spalling, efflorescence, slow and weather-dependent construction).
1. Relation between unit and mortar — the mechanism
Consequences:
- Masonry strength is only about 25–50% of the unit strength.
- Increasing the mortar strength gives a less than proportionate gain — doubling the mortar strength may raise the masonry strength by only 15–25%.
- A thinner bed joint gives a stronger wall.
- The mortar should be weaker than the unit — a mortar stronger than necessary is wasteful, cracks the units rather than the joints, and gives brittle unrepairable failure.
- Empirically fk = K fb0.7 fm0.3 — unit strength matters more than twice as much as mortar strength.
Sketch: a masonry prism under compression with arrows showing the mortar squeezing outwards, the unit in lateral tension, and vertical splitting cracks through the bricks.
2. Factors affecting the compressive strength — four groups
| Group | Factor | Effect |
|---|---|---|
| A. Unit | Strength of the unit | The single most important factor. |
| Shape / height-to-width ratio as laid | Taller unit → fewer bed joints → stronger masonry (factor kp). | |
| Frogs, perforations, voids | Reduce net area, cause stress concentration. | |
| Water absorption / suction rate | A dry absorbent brick sucks water from the mortar and destroys the bond — bricks must be soaked. | |
| B. Mortar | Grade and strength | Increases strength, but far less than proportionately. |
| Mix proportion and workability | Richer than 1:3 shrinks and cracks; leaner than 1:6 is harsh and segregates. | |
| Water retentivity, deformability | A more deformable mortar increases the lateral tension in the unit. | |
| C. Geometry | Thickness of the mortar joint | Very significant — a 20 mm joint can lose 20–30% of the strength. |
| Slenderness ratio | Higher SR → buckling → permissible stress reduced by ks. | |
| Eccentricity of loading | Adds bending; permissible stress reduced by ks. | |
| Cross-sectional area | Small sections lack redundancy → ka = 0.7 + 1.5A. | |
| D. Workmanship | Bond pattern, corner interlocking | Continuous vertical joints split the wall into independent leaves. |
| Filling of head (vertical) joints | Unfilled perpends are the commonest defect. | |
| Uniformity of bed joints, verticality | Uneven joints cause stress concentration; out-of-plumb walls add eccentricity. | |
| Curing, age, rate of construction | Green mortar overloaded by building too fast. |
Design consequence: this is why IS 1905 writes fper = fb ks ka kp.
Question 3
From the figure: the pier is 200 mm wide and projects 100 mm on each face, so the pier thickness tp = tw + 100 + 100; piers at 4.0 m centres.
Assume: wall thickness tw = 230 mm (one brick); masonry 20 kN/m³; interior wall → e = 0. Design one bay.
Note: at Sp/Wp = 20 the piers provide no stiffening — they only add 40 000 mm² of bearing area per bay. To gain a stiffening coefficient the spacing would have to be reduced below 4 m.
Question 4
Assume: two leaves of 115 mm (half brick) each with a 50 mm cavity, tied with metal ties → overall 280 mm; RCC slab 120 mm; masonry 20 kN/m³; the floor and roof bear on the inner leaf only. Design the ground-floor wall (worst case), per metre run.
Question 5
Assume: t = 230 mm; masonry 20 kN/m³. Design a 1 m run of wall.
The wall is anchored at the floor and the roof, so it is treated as partially constrained at both ends; the moment is critical at the base and at mid-height:
Note: because wind is present, IS 1905 also permits the permissible stresses to be increased by one third — not needed here, so the design is conservative.
Question 6
Assume: t = 230 mm; masonry 20 kN/m³; unit 5 N/mm² with M1 mortar.