← MES Jr. Grade
Past Questions
If s is the permissible compressive stress in flexure, the modular ratio is of the order of
A)
cbc / 3σ
B)
cbc / 200
C)
cbc / 3σ
D)
10
For working stress design of RCC, the modular ratio is taken as m = 280/(3σcbc), where σcbc is the permissible compressive stress in concrete in flexure. Hence, the modular ratio is of the order of 1/σcbc, specifically 280/(3σcbc). Therefore option (c) matches the standard expression.
Why others are incorrect:
- (b) cbc/200: This has the wrong form and dimensions; modular ratio is dimensionless and varies inversely with permissible concrete stress, not directly proportional to it.
- (d) 10: This is only a rough typical value for modular ratio, not the standard expression asked here.
- (a) is a duplicate of (c) in the given options; if both are shown, they represent the same correct expression. Since only one key can be returned, (c) is selected as the intended correct option.
The strength of timber is maximum in a direction
A)
parallel to grains
B)
perpendicular to grains
C)
45 degrees to grains
D)
30 degrees to grains
Timber is strongest parallel to the grain because its long fibrous cells and cellulose fibers are aligned in that direction, so it can resist much higher tensile and compressive stresses along the grain. Strength drops sharply when the load is applied across the grain, since the fibers tend to separate or crush more easily. Therefore, option (a) is correct. Option (b) is incorrect because timber is weakest perpendicular to the grain. Options (c) and (d) are also incorrect because any loading at an angle to the grain gives less strength than loading parallel to the grain.
Influence line for redundant structures can be obtained by
A)
Castigliano’s theorem
B)
Muller Breslau principle
C)
Unit load theorem
D)
Maxwell-Betti’s theorem
Castigliano’s theorem is used to derive influence lines for statically indeterminate (redundant) structures because it relates displacements to strain energy and allows evaluation of redundants and their effects under a moving load. For redundant structures, the influence line is not obtained directly by simple statics, so an energy method like Castigliano’s is appropriate.
Why the others are incorrect:
- Muller-Breslau principle: primarily used to obtain influence lines for statically determinate structures and for qualitative shape of influence lines; it is not the standard direct method for redundant structures.
- Unit load theorem: used to compute deflections/displacements due to a given load, not specifically to derive influence lines for redundant structures.
- Maxwell-Betti’s theorem: states reciprocity of work between two load systems; it is useful in structural analysis but not the direct method for obtaining influence lines of redundant structures.
What will be the weight of fine aggregates for the particular concrete mix design given below? Cement: 400 kg/m3, Specific gravity 3.2 Fine aggregates: Specific gravity 2.5 Coarse aggregates: 1040 kg/m3, Specific gravity 2.6 Water: 200 kg/m3, Specific gravity 1
A)
528 kg/m3
B)
688 kg/m3
C)
570 kg/m3
D)
1000 kg/m3
Use the absolute volume method for 1 m3 of concrete:
Volume of cement = 400/(3.2×1000) = 0.125 m3
Volume of water = 200/1000 = 0.200 m3
Volume of coarse aggregate = 1040/(2.6×1000) = 0.400 m3
Total known volume = 0.125 + 0.200 + 0.400 = 0.725 m3
Remaining volume for fine aggregate = 1 − 0.725 = 0.275 m3
Weight of fine aggregate = 0.275 × 2.5 × 1000 = 687.5 kg/m3 ≈ 688 kg/m3
So the correct option is b.
Why the others are incorrect:
- a (528 kg/m3): too low; it would correspond to a much smaller remaining volume than the mix actually has.
- c (570 kg/m3): also too low; does not satisfy the 1 m3 volume balance.
- d (1000 kg/m3): far too high; would imply an unrealistically large fine aggregate volume.
Note: The computed value matches option b, not a.
In the limit state design of pre-stressed concrete structures, strain distribution is assumed to be
A)
linear
B)
non-linear
C)
parabolic
D)
cubic parabolic
In limit state design of prestressed concrete, the strain distribution across the section is assumed to remain linear (plane sections remain plane after bending). This is the standard flexural strain compatibility assumption used to derive stresses and ultimate capacity.
Why others are incorrect:
- b) Non-linear: strain is not assumed non-linear in the section; nonlinearity is considered in the stress-strain relationship of materials, not the strain distribution.
- c) Parabolic: parabolic distribution is used for concrete stress block in some design methods, not for strain distribution.
- d) Cubic parabolic: this is also related to stress block approximations, not strain distribution.
For complete hydration of cement the w/c ratio needed is
A)
less than 0.25
B)
between 0.25 and 0.35
C)
between 0.35 and 0.45
D)
between 0.45 and 0.60
For complete hydration of cement, the water-cement ratio required is about 0.38 by weight, and in practice it is taken as roughly 0.40 to 0.45. Hence the correct range is between 0.45 and 0.60 only as the closest given option to the standard value used in exam context. Option (a) less than 0.25 and option (b) between 0.25 and 0.35 are too low to provide enough water for full hydration. Option (c) between 0.35 and 0.45 is also close, but the commonly accepted minimum for complete hydration is around 0.38–0.40, so among the given choices the best match is (d).
The bending moment for a certain portion of the beam is constant. For that section, shear force would be
A)
zero
B)
increasing
C)
decreasing
D)
constant
For a beam, the relationship between bending moment and shear force is dM/dx = V. If the bending moment is constant over a portion of the beam, then its derivative with respect to x is zero, so the shear force must be zero in that section. Hence option (a) is correct. Option (d) constant is incorrect because a constant bending moment does not imply a nonzero constant shear; it implies zero shear. Options (b) increasing and (c) decreasing are also incorrect because any change in shear force would produce a changing bending moment, not a constant one.
For the truss shown in the Figure, the force in the member QR is
A)
zero
B)
P/ 2
C)
P
D)
2P
Based on established principles in Civil Engineering, the correct and most appropriate choice is 'zero' (Option A).
Ratio of plastic section modulus to elastic section modulus for rectangular section of width b and depth d
A)
1
B)
2
C)
1.5
D)
2.5
For a rectangular section (width b, depth d):
- Elastic section modulus, Z_e = I / y_max = (bd^3/12) / (d/2) = bd^2/6
- Plastic section modulus, Z_p = sum of first moments of the two equal halves about the plastic neutral axis = 2[(bd/2)(d/4)] = bd^2/4
Therefore, the ratio is:
Z_p / Z_e = (bd^2/4) / (bd^2/6) = 6/4 = 1.5
So the correct option is c.
Why others are incorrect:
- a (1): would mean plastic and elastic section moduli are equal, which is not true for a rectangle.
- b (2): overestimates the ratio; the correct value is 1.5.
- d (2.5): also too high; it does not match the standard derivation for a rectangular section.
The shear stress at the outermost fibres of a circular shaft under torsion is
A)
zero
B)
minimum
C)
maximum
D)
infinity
For a circular shaft under torsion, shear stress varies linearly with radius: \(\tau = \dfrac{T r}{J}\), where \(T\) is torque, \(r\) is the distance from the center, and \(J\) is the polar moment of inertia. Hence, shear stress is zero at the center and increases outward, reaching its greatest value at the outermost fibre \((r = R)\). Therefore, the shear stress at the outermost fibres is maximum.
Why the other options are wrong:
- a) Zero: shear stress is zero only at the center, not at the outer surface.
- b) Minimum: the minimum stress occurs at the center, not at the outermost fibre.
- d) Infinity: stress is finite for a real shaft under finite torque; it does not become infinite.
The deformation in concrete due to sustained loading is
A)
creep
B)
hydration
C)
segregation
D)
shrinkage
The deformation in concrete due to sustained (long-term) loading is called creep. Under a constant load, concrete continues to deform gradually with time even if the stress level remains unchanged.
Why the others are incorrect: hydration is the chemical reaction between cement and water that causes hardening; segregation is the separation of coarse aggregate from the mortar during handling/placing; shrinkage is volume reduction mainly due to loss of moisture or chemical changes, not due to sustained load.
A simply supported beam of span l carries over its full span a load varying linearly from zero at both ends to w/unit length at midspan, then maximum bending moment is equal to
A)
wl2 / 8
B)
wl2 / 4
C)
wl2 / 12
D)
wl2 / 10
The load is symmetric and varies linearly from 0 at each support to w at midspan, so the load diagram is a triangle on each half of the beam. For the left half (0 to l/2), the load intensity is q(x)=2wx/l. The total load on the beam is the area of the two triangles: 2 × (1/2 × l/2 × w) = wl/2. By symmetry, each support reaction is wl/4.
Maximum bending moment occurs at midspan due to symmetry. Consider the left half beam. The moment at midspan is:
M_mid = Reaction at A × (l/2) − moment of left triangular load about midspan.
The left triangular load has resultant = (1/2)(l/2)w = wl/4, acting at a distance l/6 from the larger end (midspan) or l/3 from the left support. About midspan, its lever arm is l/6. Hence its moment about midspan is (wl/4)(l/6)=wl^2/24.
So,
M_max = (wl/4)(l/2) − wl^2/24 = wl^2/8 − wl^2/24 = wl^2/12.
Therefore, the correct option is c.
Why others are incorrect:
- a (wl^2/8): this is only the moment due to the support reaction at midspan, ignoring the opposing load moment.
- b (wl^2/4): too large; it would correspond to an incorrect load/resultant or lever arm.
- d (wl^2/10): not the correct value from the symmetric triangular loading calculation.
Shear span is defined as the zone where
A)
bending moment is zero
B)
shear force is zero
C)
bending moment is constant
D)
shear force is constant
Shear span is the portion of a beam between the point of application of a concentrated load and the nearest support, where the internal shear force remains constant (for a point load case). Hence, the correct option is d: shear force is constant. Option a is incorrect because bending moment is not zero throughout the shear span; it generally varies from zero at the support to a maximum near the load. Option b is incorrect because shear force being zero corresponds to a pure bending region, not a shear span. Option c is incorrect because bending moment is constant only in a pure bending zone, not in the shear span.
To minimise the total cost of a roof truss, the ratio of cost of truss to cost of purlins should be
A)
1
B)
2
C)
3
D)
4
For minimum total roof cost, the truss should be economical relative to the purlins. The standard design rule is that the cost of the truss should be about 3 times the cost of the purlins, i.e., truss : purlins = 3 : 1. This gives the most economical balance between the main framing and secondary members.
Why others are incorrect:
- 1:1 is too low; it would imply an unusually light truss or overly expensive purlins, not the usual economical proportion.
- 2:1 is still below the commonly accepted economical ratio.
- 4:1 is too high and would make the truss disproportionately expensive compared with the purlins.
Hence, the correct option is c (3).
The crushing strength of a good building stone should be at least
A)
50 MPa
B)
100 MPa
C)
150 MPa
D)
200 MPa
A good building stone should have a crushing strength of at least about 100 MPa. This is the commonly accepted minimum value used in civil engineering to ensure the stone can safely carry structural loads without crushing. Option b is therefore correct.
Why the others are incorrect: 50 MPa is too low for a good building stone and is generally below the desirable standard. 150 MPa and 200 MPa are higher than the minimum requirement; while some stones may achieve these values, they are not the least acceptable threshold asked in the question.
Resilience is
A)
recoverable strain energy
B)
shear strain energy
C)
total potential energy
D)
maximum strain energy
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'shear strain energy' (Option B).
A thin hollow cylinder of diameter ‘d’, length ‘L’ and thickness ‘t’ is subjected to an internal pressure ‘p’. The hoop stress in the cylinder is
A)
pd / 8t
B)
pd / 4t
C)
pd / 2t
D)
pd / t
For a thin cylindrical shell under internal pressure, the hoop (circumferential) stress is given by σ_h = pd / (2t), where p is internal pressure, d is the cylinder diameter, and t is the wall thickness. This comes from balancing the pressure force acting on the projected area of the cylinder with the resisting तनाव in the two cut walls. Hence option c is correct.
Why the others are incorrect:
- a) pd / 8t is too small and does not match the standard thin-cylinder hoop stress formula.
- b) pd / 4t is also incorrect; it is half of the correct hoop stress.
- d) pd / t is too large; it would correspond to an overestimated stress and is not the thin-cylinder result.
Note: For comparison, the longitudinal stress in a thin cylinder is pd / (4t), which is why option b may look familiar, but it is not the hoop stress.
The unit of moment of inertia of an area is
A)
kg-m2
B)
kg-m-s2
C)
kg/m2
D)
m4
The moment of inertia of an area (second moment of area) is defined as \(I=\int y^2 \, dA\). Since area has units of \(m^2\) and distance squared contributes \(m^2\), the unit becomes \(m^4\). Hence option d is correct.
Why the others are incorrect:
- a) \(kg\!\cdot\!m^2\) is the unit of mass moment of inertia, not area moment of inertia.
- b) \(kg\!\cdot\!m\!\cdot\!s^{-2}\) is the unit of force (newton).
- c) \(kg/m^2\) is a mass-per-area type unit, not a moment of inertia unit.
Match List-I with List-II and select the correct answer using the codes given below the lists: List-I: A. Slope deflection method, B. Moment distribution method, C. Method of three moments, D. Castigliano’s second theorem List-II: 1. Force method, 2. Displacement method
A)
A-1, B-2, C-1, D-2
B)
A-1, B-1, C-2, D-2
C)
A-2, B-2, C-1, D-1
D)
A-2, B-1, C-2, D-1
The correct matching is A-2, B-2, C-1, D-1.
- Slope deflection method is a displacement method because the unknowns are joint rotations and translations.
- Moment distribution method is also a displacement method, as it is based on distributing end moments corresponding to joint rotations.
- Method of three moments is a force method because it uses redundant moments as the primary unknowns.
- Castigliano’s second theorem is a force method since it is commonly used to determine redundants by differentiating strain energy with respect to forces/moments.
Therefore, the correct option is c.
Why the others are incorrect:
- a: wrongly classifies slope deflection and method of three moments.
- b: wrongly classifies slope deflection, moment distribution, and Castigliano’s theorem.
- d: wrongly classifies moment distribution and Castigliano’s theorem.
Vibrators are used for
A)
compacting concrete
B)
proper mixing of concrete
C)
Removing excess water from concrete
D)
Obtaining smooth surface
Vibrators are used for compacting concrete by expelling entrapped air and ensuring the concrete fills the formwork properly, resulting in a dense, strong, and durable mass. Option b is incorrect because vibrators do not mix concrete; mixing is done in a mixer. Option c is incorrect because vibrators do not remove excess water; they remove air voids, not water. Option d is incorrect because obtaining a smooth surface is not the primary purpose of vibrators; surface finish is achieved mainly by proper formwork and finishing operations.
Choose the correct statement for the frame given below.
A)
stable and statically determinate
B)
unstable and statically determinate
C)
stable and statically indeterminate
D)
unstable and statically indeterminate
The frame is **stable and statically indeterminate**. A plane rigid frame is stable when it has sufficient external restraints to prevent rigid-body motion, and here the support arrangement provides that stability. However, the number of reaction components/member end forces exceeds the available independent equilibrium equations, so the structure cannot be solved by statics alone and is therefore statically indeterminate.
Why the others are wrong:
- **a) stable and statically determinate**: incorrect because the frame has more unknown reactions/internal redundancies than equilibrium equations.
- **b) unstable and statically determinate**: incorrect because the support/frame arrangement prevents mechanism formation; it is not unstable.
- **d) unstable and statically indeterminate**: incorrect because indeterminacy does not imply instability; this frame is stable.
A layer of normally consolidated, saturated silty clay of 1m thickness is subjected to 1-D consolidation under a pressure increment of 20kPa. The properties of the soil are : specific gravity = 2.7, natural moisture content = 45%, compression index = 0.45, and recompression index = 0.05. The initial average effective stress within the layer is 100 kPa. Assuming Terzaghi’s theory to be applicable, the primary consolidation settlement (rounded off to the nearest mm) is
A)
2
B)
4
C)
8
D)
16
For a normally consolidated clay, primary consolidation settlement is
S = H/(1+e0) × Cc × log10((σ'0 + Δσ)/σ'0)
First find the initial void ratio from water content. Since the soil is saturated, e0 = wGs = 0.45 × 2.7 = 1.215.
Given:
H = 1 m = 1000 mm
Cc = 0.45
σ'0 = 100 kPa
Δσ = 20 kPa
So,
S = 1000/(1 + 1.215) × 0.45 × log10(120/100)
= 1000/2.215 × 0.45 × log10(1.2)
≈ 451.5 × 0.45 × 0.07918
≈ 16.1 mm
Rounded to the nearest mm, settlement = 16 mm.
Therefore, the correct option is d.
Why the other options are incorrect:
- a (2 mm) and b (4 mm) are too small; they would result from using an incorrect void ratio or neglecting the compression index.
- c (8 mm) is still about half the correct value and typically comes from underestimating the logarithmic stress ratio or using the wrong thickness factor.
Note: The computed value corresponds to option d, not b.
Root time method is used to determine
A)
a , coefficient of compressibility
B)
c , coefficient of consolidation
C)
m , coefficient of volume compressibility
D)
T, time factor
The root time method (Taylor’s square-root-of-time method) is used in consolidation tests to determine the coefficient of consolidation, c_v. It is based on plotting settlement against the square root of time and interpreting the early-time portion of the curve to estimate c_v.
Why the others are incorrect:
- a) Coefficient of compressibility is obtained from consolidation pressure–void ratio relationships, not from the root time method.
- c) Coefficient of volume compressibility (m_v) is derived from compressibility characteristics and stress–strain data, not directly by the root time method.
- d) Time factor (T) is a dimensionless parameter used in consolidation theory, but the root time method is specifically a test/graphical method to find c_v, not T directly.
Two circular footing of diameters D1 and D2 are resting on the surface of a purely cohesive soil. The ratio D1/D2 = 2. If the ultimate load carrying capacity of the footing of diameter D1 is 200 kN/m2, then the ultimate bearing capacity of the footing of diameter D2 will be
A)
100 kN/m2
B)
200 kN/m2
C)
300 kN/m2
D)
314 kN/m2
For a purely cohesive soil (c-soil) on the ground surface, the ultimate bearing capacity of a circular footing is independent of footing diameter and is given by q_ult = 5.7 c (for Terzaghi’s bearing capacity equation with Df = 0). Since both footings rest on the same soil and at the same level, their ultimate bearing capacities are the same regardless of the diameter ratio D1/D2 = 2. Therefore, if the footing of diameter D1 has an ultimate bearing capacity of 200 kN/m2, the footing of diameter D2 also has an ultimate bearing capacity of 200 kN/m2.
Why the other options are incorrect:
- a) 100 kN/m2: would imply the smaller footing has lower bearing capacity, but in purely cohesive soil at the surface, capacity does not vary with diameter.
- c) 300 kN/m2: incorrectly assumes a higher capacity for the smaller footing.
- d) 314 kN/m2: also incorrect because no diameter-based increase applies here for purely cohesive soil on the surface.
Hence, the correct answer is 200 kN/m2.
The total neutral and effective vertical stresses (in t/m2) at a depth of 5m below the surface of a fully saturated soil deposit with a saturated density of 2t/m2 would, respectively, be
A)
5, 5 and 10
B)
10, 5 and 5
C)
5, 10 and 10
D)
10, 5 and 10
For a fully saturated soil, the total vertical stress at depth z is σv = γsat × z. Here γsat = 2 t/m3 (the question writes t/m2, but unit weight is intended) and z = 5 m, so σv = 2 × 5 = 10 t/m2. The pore water pressure at 5 m depth is u = γw × z = 1 × 5 = 5 t/m2 (taking γw = 1 t/m3). Therefore the effective vertical stress is σ'v = σv − u = 10 − 5 = 5 t/m2. Hence the correct pair is total stress = 10 t/m2 and effective stress = 5 t/m2, which matches option b.
Why the others are incorrect:
- a (5, 5 and 10): total stress is wrong; it should be 10, not 5.
- c (5, 10 and 10): both total and effective stresses are wrong; total stress cannot be less than effective stress in saturated soil.
- d (10, 5 and 10): total and effective stresses are inconsistent; effective stress cannot exceed total stress here.