← 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.
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).
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.
When a bar is subjected to a change of temperature and its deformation is prevented, the stress induced in the bar is
A)
tensile stress
B)
compressive stress
C)
shear stress
D)
thermal stress
When a bar is heated or cooled and its free expansion or contraction is fully prevented, internal stress develops due to the restrained thermal strain. This is called thermal stress. If the temperature rises, the bar tends to expand but is restrained, so compressive stress is induced; if the temperature falls, it tends to contract but is restrained, so tensile stress is induced. Since the question asks for the stress induced due to change in temperature with deformation prevented, the general correct term is thermal stress.
Why others are incorrect: (a) tensile stress is only one possible result, specifically for cooling, not the general name; (b) compressive stress occurs only for heating, not always; (c) shear stress is not produced by uniform temperature change in a restrained bar.
For an isotropic material, the relationship between Young’s modulus (E), shear modulus (G) and Poisson’s ratio (v) is given by
A)
G = E / 2(1+v)
B)
E = G / 2(1+v)
C)
G = E / (1+2v)
D)
G = E / 2(1-2v)
For an isotropic, linear elastic material, the standard elastic relation is E = 2G(1+v). Rearranging gives G = E / [2(1+v)], which matches option a. Option b is incorrect because it is the inverse form written wrongly as E = G / 2(1+v) instead of E = 2G(1+v). Option d is incorrect because G = E / [2(1-2v)] is not the Young’s modulus–shear modulus relation; it is associated with bulk modulus-type relations. Option c is incorrect because the denominator should be 2(1+v), not (1+2v).
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).
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).
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.
Which of the following concepts is the basis principle of structural design based?
A)
Weak column and strong beam
B)
Equally strong column-beam
C)
Strong column and weak beam
D)
None of these
The correct principle is **strong column and weak beam**. In structural design, especially for earthquake-resistant reinforced concrete frames, beams are intentionally designed to yield before columns. This creates a ductile failure mechanism and helps prevent sudden collapse by allowing energy dissipation through beam hinging while keeping the columns stable and the overall frame standing.
Why the others are incorrect:
- **a. Weak column and strong beam**: This is unsafe because column failure can lead to story collapse and a brittle, catastrophic mechanism.
- **b. Equally strong column-beam**: This does not ensure the desired ductile behavior; if columns are not stronger than beams, the structure may still form undesirable column hinges.
- **d. None of these**: Incorrect because the recognized design concept is clearly strong column and weak beam.
For mass concrete work such as a dam, the recommended type of cement is
A)
Ordinary Portland cement
B)
Quick setting cement
C)
Low-heat Portland cement
D)
Portland Pozzolona cement
Low-heat Portland cement is recommended for mass concrete works such as dams because large concrete sections generate significant heat of hydration. Using low-heat cement reduces temperature rise, minimizes thermal stresses, and helps prevent cracking. Quick setting cement is meant for rapid setting, not heat control. Ordinary Portland cement produces more heat than desirable in mass concrete. Portland pozzolana cement is also useful for reduced heat and durability, but the standard recommended answer for mass concrete like dams is low-heat Portland cement.
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.
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.
A large force acting over a short period of time is called
A)
moment
B)
impulse
C)
momentum
D)
power
A large force acting over a short time interval is called an impulse. In mechanics, impulse is the product of force and the time for which it acts, and it equals the change in momentum. The other options are incorrect: momentum is mass × velocity, power is the rate of doing work, and moment is the turning effect of a force about a point.
For a reinforced concrete section, the shape of shear stress diagram is
A)
wholly rectangular
B)
wholly parabolic
C)
wholly linear
D)
rectangular and parabolic
Based on established principles in Civil Engineering, the correct and most appropriate choice is 'rectangular and parabolic' (Option D).
Match List-I with List-II and select the correct answer using the codes given below the lists: List-I: A. Serviceability, B. Shear key, C. Shrinkage, D. Concrete spalling List-II: 1. Sliding, 2. Deflection, 3. Cracking, 4. Corrosion
A)
A-1, B-3, C-4, D-2
B)
A-2, B-1, C-3, D-4
C)
A-1, B-3, C-2, D-4
D)
A-2, B-1, C-4, D-3
The correct matching is A-2, B-1, C-3, D-4.
- Serviceability is mainly concerned with excessive deflection, so A matches 2.
- A shear key is provided to resist sliding between structural parts, so B matches 1.
- Shrinkage in concrete commonly causes cracking, so C matches 3.
- Concrete spalling is often a result of reinforcement corrosion and the resulting expansion, so D matches 4.
Why the other options are wrong:
- Option a: A-1 is wrong because serviceability relates to deflection, not sliding.
- Option c: A-1 and B-3 are both wrong; serviceability is not sliding, and shear key is not cracking.
- Option d: C-4 is wrong because shrinkage leads to cracking, not corrosion; D-3 is wrong because spalling is associated with corrosion, not cracking directly.
Which one of the following aggregate gives the maximum strength in concrete?
A)
Rounded aggregate
B)
Elongated aggregate
C)
Flaky aggregate
D)
Cubical aggregate
Cubical aggregate gives the maximum strength in concrete because its particles have better interlocking, lower void content, and a more favorable shape for bonding with cement paste. This improves the load transfer and overall compressive strength of concrete. Rounded aggregate is easier to work with but provides less interlocking and bond strength than cubical aggregate. Elongated and flaky aggregates are undesirable because they create weak planes, reduce packing density, increase voids, and generally lower the strength and durability of concrete.
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.
The Le Chatelier apparatus is used to determine
A)
soundness of cement
B)
fineness of cement
C)
setting time of cement
D)
compressive strength of cement
Le Chatelier apparatus is used to determine the soundness of cement, i.e., the tendency of cement to undergo excessive expansion after setting due to free lime or magnesia. In the test, the expansion of the cement paste is measured using the split mould of the Le Chatelier apparatus.
Why the other options are incorrect:
- b) Fineness of cement is determined by sieve analysis, air permeability (Blaine) test, or residue on sieve, not by Le Chatelier apparatus.
- c) Setting time of cement is determined by Vicat apparatus, not Le Chatelier apparatus.
- d) Compressive strength of cement is determined using mortar cubes tested in a compression testing machine, not Le Chatelier apparatus.
In a concrete mix, if the maximum size of coarse aggregate is increased, the proportion of fine to coarse aggregate should be
A)
increased
B)
decreased
C)
kept the same
D)
not dependent on size of aggregates
When the maximum size of coarse aggregate is increased, the total surface area of aggregate particles decreases. Therefore, less fine aggregate (sand) is needed to fill voids and provide workability, so the proportion of fine to coarse aggregate should be decreased. Option (a) is incorrect because increasing the fine aggregate would be unnecessary and would reduce economy/workability balance. Option (c) is incorrect because the proportion does depend on aggregate size. Option (d) is incorrect for the same reason: mix proportions are affected by the maximum size of aggregate.
The material that exhibits the same elastic properties in all directions at a point is said to be
A)
homogeneous
B)
orthotropic
C)
viscoelastic
D)
isotropic
A material that has the same elastic properties in all directions at a point is called isotropic. In an isotropic material, properties like Young’s modulus, shear modulus, and Poisson’s ratio are direction-independent.
Why the others are incorrect:
- Homogeneous means the material has the same properties at every point in the body, but not necessarily in every direction.
- Orthotropic means the material has different properties along three mutually perpendicular directions.
- Viscoelastic refers to materials that show both elastic and time-dependent viscous behavior; it does not describe directional uniformity of elastic properties.
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.
For a given shear force across a symmetrical I section, the intensity of shear stress is maximum at
A)
extreme fibres
B)
centroid of the section
C)
at the junction of the flange and the web but on the web
D)
at the junction of the flange and the web but on the flange
For a symmetrical I-section under a given shear force, the shear stress distribution is given by \(\tau = \frac{VQ}{Ib}\). In an I-section, the flange is wide, so shear stress there is relatively low, while the web is narrow, causing the same shear force to produce a much higher stress. The maximum shear stress occurs at the junction of the flange and the web, and specifically just inside the web, because the web carries most of the shear.
Why the others are incorrect:
- a) Extreme fibres: shear stress is zero at the top and bottom free surfaces.
- b) Centroid of the section: this is not where maximum shear stress occurs in an I-section; the maximum is in the web near the neutral axis, not necessarily at the centroid.
- d) At the junction but on the flange: shear stress is lower in the flange due to its larger width; the peak occurs on the web side of the junction.
Hence, the correct answer is c) at the junction of the flange and the web but on the web.
A long shaft of diameter ‘d’ is subjected to twisting moment T at its ends. The maximum normal stress at its cross-section is
A)
Zero
B)
16T / πd3
C)
32T / πd3
D)
64T / πd3
For a circular shaft subjected to a pure twisting moment T, the stress developed is only shear stress, not normal stress. The torsion formula gives maximum shear stress at the outer surface as \u03c4_max = 16T/(\u03c0d^3). Since torsion does not produce direct normal stress in a long circular shaft, the maximum normal stress at the cross-section is zero.
Why the other options are incorrect:
- b) 16T/(\u03c0d^3) is the maximum shear stress, not normal stress.
- c) 32T/(\u03c0d^3) is not the normal stress for pure torsion; it is not applicable here.
- d) 64T/(\u03c0d^3) is also incorrect and does not represent the normal stress in a shaft under pure twisting moment.
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.