UPSC IES/ESE (Engineering Services) Geotechnical, Structural and Transportation Engineering Syllabus

How do Terzaghi's bearing capacity factors change for local shear failure, and which soils exhibit it?

Local (and punching) shear failure occurs in loose sands and soft clays (low relative density/high compressibility). Strength parameters are reduced: $c_m=\frac{2}{3}c$ and $\tan\phi_m=\frac{2}{3}\tan\phi$, and the corresponding reduced factors $N_c', N_q', N_\gamma'$ are used.

State Rankine's coefficients of active and passive earth pressure for a cohesionless backfill with horizontal ground.

$$K_a=\frac{1-\sin\phi}{1+\sin\phi}=\tan^{2}\!\left(45^\circ-\frac{\phi}{2}\right),\quad K_p=\frac{1+\sin\phi}{1-\sin\phi}=\tan^{2}\!\left(45^\circ+\frac{\phi}{2}\right)$$ Note $K_p=\frac{1}{K_a}$.

Give the active earth pressure distribution for a cohesive ($c$–$\phi$) soil and the depth of tension crack.

$$\sigma_a = K_a\gamma z - 2c\sqrt{K_a}$$ The pressure is zero (and tension above) at the critical depth $z_0=\frac{2c}{\gamma\sqrt{K_a}}$. For $\phi=0$: $z_0=\frac{2c}{\gamma}$.

For a purely cohesive saturated clay ($\phi=0$), what is the ultimate bearing capacity of a strip footing at the surface (Terzaghi / Prandtl)?

$N_c=5.7$ (Terzaghi strip) or $N_c=(\pi+2)=5.14$ (Prandtl/Skempton surface), with $N_q=1$, $N_\gamma=0$. So $q_u=cN_c+\gamma D_f$; net $q_{nu}=cN_c$.

Give the static pile capacity formula (in general form) for a single pile.

$$Q_u = Q_p + Q_s = q_p A_p + \sum f_s A_s$$ End-bearing $Q_p=A_p(cN_c+q'N_q)$; skin friction $Q_s=\sum (\alpha c + K\sigma_v'\tan\delta)A_s$. Allowable load $Q_a=\frac{Q_u}{F}$ (F typically 2.5).

What is negative skin friction on a pile and what causes it?

Negative skin friction is downward drag force on a pile caused by surrounding soil settling more than the pile (e.g., consolidating fill or lowered water table). It ADDS to the load on the pile, reducing its net allowable capacity rather than helping support it.

Define the factor of safety for slope stability and state the form for a Swedish (Fellenius) circle.

$$F = \frac{\text{Resisting moment}}{\text{Driving moment}}$$ For the ordinary method of slices: $F=\frac{\sum (c'\,l + (N-u\,l)\tan\phi')}{\sum W\sin\alpha}$, where $N=W\cos\alpha$ is the normal force on each slice base.

Define Taylor's stability number $S_n$ for slope stability analysis.

$$S_n=\frac{c_m}{\gamma H}=\frac{c}{F_c\,\gamma H}$$ where $c_m$ = mobilized cohesion, $\gamma$ = unit weight, $H$ = slope height. It is dimensionless and obtained from Taylor's charts as a function of slope angle and $\phi$.

State the equation for static determinacy of a plane (2D) pin-jointed truss.

A plane truss is statically determinate when $m + r = 2j$, where $m$ = number of members, $r$ = number of reaction components, $j$ = number of joints. If $m+r>2j$ it is indeterminate; if $m+r<2j$ it is a mechanism (unstable).

Give the degree of static indeterminacy formulas for plane and space rigid-jointed frames.

Plane frame: $D_s = 3m + r - 3j$ (external $=r-3$, internal $=3c$ for closed loops). Space frame: $D_s = 6m + r - 6j$. Here $m$ = members, $r$ = reactions, $j$ = joints.

Define kinematic indeterminacy (degree of freedom) for plane and space rigid frames.

Kinematic indeterminacy $D_k$ = number of independent joint displacements. Plane frame: $D_k=3j-r$ (3 DOF per joint: 2 translations + 1 rotation). Space frame: $D_k=6j-r$. (Reduce by axial-rigidity constraints if members are inextensible.)

State the slope-deflection equation for a prismatic member AB.

$$M_{AB}=\frac{2EI}{L}\left(2\theta_A+\theta_B-3\psi\right)+M_{AB}^{F}$$ where $\theta_A,\theta_B$ = end rotations, $\psi=\frac{\Delta}{L}$ = chord rotation (sway), and $M_{AB}^{F}$ = fixed-end moment.

Define distribution factor and carry-over factor in the moment distribution method.

Distribution factor for a member at a joint $=\frac{k}{\sum k}$, where stiffness $k=\frac{4EI}{L}$ (far end fixed) or $\frac{3EI}{L}$ (far end pinned). Carry-over factor = $\frac{1}{2}$ for a prismatic member with the far end fixed (carries half the applied moment).

Give the fixed-end moments for a fixed beam of span $L$ under (a) central point load $W$ and (b) UDL $w$.

(a) Central point load: $M_{AB}=-M_{BA}=\frac{WL}{8}$. (b) Uniformly distributed load: $M_{AB}=-M_{BA}=\frac{wL^{2}}{12}$. (Signs per the sagging/hogging convention used.)

What is an influence line diagram, and what does Muller–Breslau's principle state?

An influence line shows the variation of a response function (reaction, shear, moment) at a fixed point as a unit load moves across the structure. Muller–Breslau principle: the influence line for a force quantity is, to scale, the deflected shape produced by removing the corresponding restraint and giving a unit displacement in its direction.

In the matrix stiffness (displacement) method, state the governing equation and the order of the global stiffness matrix.

$$\{P\}=[K]\{\delta\}$$ where $\{P\}$ = joint loads, $[K]$ = global stiffness matrix, $\{\delta\}$ = joint displacements. The order of $[K]$ equals the number of degrees of freedom (kinematic indeterminacy).

For a simply supported beam of span $L$ crossed by a single moving point load $W$, where is the absolute maximum bending moment and its value?

Absolute maximum bending moment occurs when the load is at midspan, giving $M_{max}=\frac{WL}{4}$ at the centre. Maximum shear occurs when the load is just inside a support, giving $V_{max}=W$.

Compare Working Stress Method (WSM) and Limit State Method (LSM) of RCC design.

WSM is a deterministic elastic method using permissible (allowable) stresses with a single factor of safety and assumes a linear stress block. LSM is a semi-probabilistic method using partial safety factors on loads and materials, checks both ultimate (strength) and serviceability limit states, and uses a rectangular-parabolic stress block — more economical and rational.

In IS 456 LSM, give the partial safety factors for loads and for materials.

Load factor for ultimate limit state (DL+LL): $1.5$. Material partial safety factors: concrete $\gamma_m=1.5$, steel $\gamma_m=1.15$. Hence design strengths: $0.446 f_{ck}$ (taken $0.45f_{ck}$) for concrete and $0.87 f_y$ for steel.

Give the limiting depth of neutral axis ratio $\frac{x_{u,max}}{d}$ for Fe 250, Fe 415 and Fe 500 steel (IS 456 LSM).

Fe 250: $\frac{x_{u,max}}{d}=0.53$. Fe 415: $\frac{x_{u,max}}{d}=0.48$. Fe 500: $\frac{x_{u,max}}{d}=0.46$. These define the balanced (limiting) section between under- and over-reinforced behaviour.

State the limiting moment of resistance of a singly reinforced rectangular section (IS 456, LSM).

$$M_{u,lim}=0.36\,f_{ck}\,b\,x_{u,max}\left(d-0.42\,x_{u,max}\right)$$ For Fe 415: $M_{u,lim}=0.138\,f_{ck}\,b\,d^{2}$. (Lever arm $z=d-0.42x_u$; compressive force $=0.36f_{ck}bx_u$.)

How are one-way and two-way slabs distinguished, and what is the load distribution?

If the ratio of longer to shorter span $\frac{L_y}{L_x}>2$, the slab is one-way (bends primarily in the short direction). If $\frac{L_y}{L_x}\le 2$, it is two-way (bends in both directions). One-way slabs carry load along the short span; two-way slabs distribute load to all four supports.

Give the short-column axial load capacity formula for an RCC column with helical/lateral ties (IS 456 LSM).

$$P_u = 0.4\,f_{ck}\,A_c + 0.67\,f_y\,A_{sc}$$ for axially loaded short columns (tied). For helically reinforced columns the capacity may be enhanced by a factor of 1.05. ($A_c$ = net concrete area, $A_{sc}$ = area of steel.)

What are the two main modes of shear failure to check in an isolated RCC footing?

(1) One-way (wide-beam) shear: critical section at distance $d$ from the face of the column. (2) Two-way (punching) shear: critical section on a perimeter at $d/2$ from the column face; permissible punching shear stress $=k_s\,0.25\sqrt{f_{ck}}$ with $k_s=0.5+\beta_c\le 1$.

For an axially loaded steel compression member, state Euler's critical buckling load and define slenderness ratio.

$$P_{cr}=\frac{\pi^{2}EI}{L_e^{2}}$$ where $L_e$ = effective length. Slenderness ratio $\lambda=\frac{L_e}{r_{min}}$, where $r_{min}=\sqrt{\frac{I_{min}}{A}}$ is the least radius of gyration. Buckling strength decreases as $\lambda$ increases.

Give effective length $L_e$ for an axially loaded column for the four ideal end conditions.

Both ends pinned: $L_e=L$. Both ends fixed: $L_e=0.5L$. One end fixed, other pinned: $L_e=0.7L$. One end fixed, other free (cantilever): $L_e=2L$.

For a steel tension member with bolt holes, state net section capacity and the staggered-hole (chain) rule.

Net area $A_{net}=(b-n\,d_h)t$ for a straight failure line. For a zigzag (staggered) failure path, add $\sum\frac{p^{2}}{4g}\,t$ per stagger: $A_{net}=\left[b-n d_h+\sum\frac{p^{2}}{4g}\right]t$, where $p$ = pitch (stagger), $g$ = gauge.

Compare bolted and welded connections in steel structures.

Bolted: faster site erection, easy dismantling/inspection, no special skill, but holes reduce net area and joints are bulkier with possible slip. Welded: continuous load path, no reduction in section, lighter and neater joints, but needs skilled labour, inspection (radiography), and induces residual stresses/distortion.

Define the strength of a fillet weld in terms of throat thickness (IS 800 LSM).

Effective throat thickness $t_t = 0.707\,s$ (for a $90^\circ$ fillet, $s$ = weld size). Design strength per unit length $=\frac{f_u}{\sqrt{3}\,\gamma_{mw}}\,t_t$, where $f_u$ = ultimate stress of weld/base metal and $\gamma_{mw}=1.25$ (shop) or $1.5$ (site).

What is prestressed concrete, and what are pre-tensioning and post-tensioning?

Prestressed concrete has internal compressive stresses introduced (via high-tensile tendons) before service loads, to counteract tensile stresses. Pre-tensioning: tendons stressed BEFORE concreting, force transferred by bond after curing. Post-tensioning: tendons stressed AFTER concrete hardens, anchored at ends; bond optional (grouted ducts).

List the major losses of prestress in pre-tensioned and post-tensioned members.

Pre-tensioning: elastic shortening of concrete, creep of concrete, shrinkage of concrete, relaxation of steel. Post-tensioning adds: friction (wobble + curvature) and anchorage slip; elastic shortening is negligible if tendons are stressed sequentially. Pre-tensioning generally has higher total losses than post-tensioning.

Name the main types of cement and the principal Bogue compounds in OPC.

Types include OPC (33/43/53 grade), PPC, rapid-hardening, low-heat, sulphate-resisting, and white cement. The four Bogue compounds: $\ce{C3S}$ (alite, early strength), $\ce{C2S}$ (belite, later strength), $\ce{C3A}$ (flash set, high heat), and $\ce{C4AF}$ (ferrite). $\ce{C3S}$ and $\ce{C2S}$ together are ~70–80% and govern strength.

Define fineness modulus of aggregate and bulking of sand.

Fineness modulus = sum of cumulative percentages retained on standard sieves divided by 100; a higher value means coarser aggregate. Bulking of sand = increase in volume of moist sand due to surface moisture films pushing grains apart (max ~20–30% at about 4–6% moisture content); it vanishes when fully saturated or oven-dry.

What are admixtures, and give examples with their functions in concrete?

Admixtures are materials added to concrete to modify properties. Plasticizers/superplasticizers reduce water demand (improve workability/strength). Accelerators (e.g., $\ce{CaCl2}$) speed setting/gain strength. Retarders delay setting (hot weather/mass concrete). Air-entraining agents improve freeze-thaw durability. Pozzolanas (fly ash, silica fume) enhance durability and reduce heat.

State Abrams' law and the role of water–cement ratio in concrete strength.

Abrams' law: for fully compacted concrete with given materials, strength is inversely related to the water–cement ratio. Lower $\frac{w}{c}$ gives higher strength (and durability), provided the mix remains workable and fully compacted. Below ~0.4 there is insufficient water for full hydration unless plasticizers are used.

Outline the steps and objective of concrete mix design (IS 10262).

Objective: produce concrete of target mean strength, workability and durability economically. Steps: (1) compute target mean strength $f_{target}=f_{ck}+1.65\,s$ (s = standard deviation); (2) select $\frac{w}{c}$ ratio; (3) determine water content and admixture; (4) calculate cement content (check minimum for durability); (5) proportion fine and coarse aggregate; (6) trial mixes and adjust.

Define workability of concrete and name the tests used to measure it.

Workability = ease with which concrete can be mixed, placed, compacted and finished without segregation. Tests: slump cone test (medium workability), compaction factor test (low workability), Vee-Bee consistometer (very low/dry mixes), and flow table test (high workability/flowable mixes).