Past Year Questions: Properties of Metals, Stress & Strain | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) PDF Download

Q1: A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (I/r) of 105, where I is the bar length and r is the radius of gyration. The coefficient of thermal expansion of steel is 12 × 10⁻⁶/^∘C. Consider the effective length of the steel bar as 0.51 and neglect the self-weight of the bar. The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles is [2024, Set-I]
(a) 250°C 
(b) 400°C 
(c) 85°C
(d) 298°C
Ans: (d)

Q2: Consider the fillet-welded lap joint shown in the figure (Not to scale). The length of the weld shown in the effective length. The welded surface meet at right angle. The weld size is 8 mm, and the permissible stress in the weld is 120MPa. What is the safe load P (in kN, rounded off to one decimal place) that can be transmitted by this welded joint ?  [2023, Set-I]
(a) 185.2
(b) 111.3
(c) 214.5
(d) 134.3
Ans: (d)
Given data, 
Weld size = 8 mm 
Permissible stress =120MPa 
Effective throat thickness, t_e = 0.7 × Weld size = 0.7 × 8 = 5.6 m
Total effective length of weld, ℓ_e = 2 × 75 + 50 = 200m 
⇒ Safe load 'P' in kN rounded upto one decimal palce 
= 5.6 × 200 × 120 × 10⁻³
= 134.4 k N 

Q3: Consider two linearly elastic rods HI and IJ, each of length b, as shown in the figure. The rods are co-linear, and confined between two fixed supports at H and J. Both the rods are initially stress free. The coefficient of linear thermal expansion is α for both the rods. The temperature of the rod IJ is raised by ΔT, whereas the temperature of rod HI remains unchanged. An external horizontal force P is now applied at node I. It is given that α = 10⁻⁶ºC⁻¹ ,ΔT = 50º C^-1, b = 2m, AE = 10⁶ N. The axial rigidities of the rods HI and IJ are 2AE and AE, respectively. [2022, Set-II] 

To make the axial force in rod HI equal to zero, the value of the external force P (in N) is _________. (round off to the nearest integer)
(a) 85
(b) 23
(c) 65
(d) 50
Ans: (d)

R_A + R_B = P  
∵ There is no axial force in rod HI 
∴ R_A= 0 
Now check for rod IJ
Now as rod IJ is fixed from both end, so net deflection due to increase in temperature will be zero.

Q4: For a linear elastic and isotropic material, the correct relationship among Young's modulus of elasticity (E), Poisson's ratio (v), and shear modulus (G) is  [2022, Set-II] 
(a)
(b)
(c)
(d)
Ans: (a)
E = 2G(1+μ) 
G = Shear modulas 
μ = Poission's ratio 
E = Young's modulus

Q5: Strain hardening of structural steel means  [2021, Set-II]
(a) experiencing higher stress than yield stress with increased deformation
(b) strengthening steel member externally for reducing strain experienced
(c) strain occurring before plastic flow of steel material
(d) decrease in the stress experienced with increasing strain
Ans: (a)
Strain hardening is experiencing higher stress than yield stress with increased deformation
In the figure AB = Strain hardening zone
OA = Linear elastic zone
Stress corresponding to point 'A' is yield stress.

Q6: A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O-P'-Q'-R' as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight.  [2021, Set-I]
The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R (in mm,round off to one decimal place) is ________
(a) 1.2
(b) 6.3
(c) 5.2
(d) 2.5
Ans: (d)
So horizontal displacement of the point (0.5 m, 0.5 m) 
= − 2.5 mm + 5 mm = 2.5 m

Q7: The state of stress represented by Mohr's circle shown in the figure is     [2020, Set-II]
(a) uniaxial tension
(b) biaxial tension of equal magnitude
(c) hydrostatic stress
(d) pure shear
Ans: (d)
In pure shear condition, Mohr's circle has its center at origin.

Q8: A rigid, uniform, weightless, horizontal bar is connected to three vertical members P, Q and R as shown in the figure. All three members have identical axial stiffness of 10 kN/mm. The lower ends of bars P and R rest on a rigid horizontal surface. When NO laod is applied, a gap of 2 mm exist between the lower end of the bar Q and the rigid horizontal surface. When a vertical load W is placed on the horizontal bar in the downward direction, the bar still remains horizontal and gets displayed by 5 mm in the vertically downward direction.  [2020, Set-I]
The magnitude of the load W (in kN, round off to the nearst integer), is ______
(a) 110
(b) 150
(c) 130
(d) 160
Ans: (c)
P₁ + P₁ + P₂ = W


Q9: The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below:  [2020, Set-I]
The correct match between the stress paths and the listed loading conditions, is
(a) OP-I, OQ-II, OR-IV, OS-III
(b) OP-IV, OQ-III, OR-I, OS-II
(c) OP-III, OQ-II, OR-I, OS-IV
(d) OP-I, OQ-III, OR-II, OS-IV
Ans: (b)

Q10: An isolated concrete pavement slab of length L is resting on a frictionless base. The temperature of the top and bottom fibre of the slab are T_t and T_b , respectively. Given: the coefficient of thermal expansion = α and the elastic modulus = E. Assuming T_t > T_b and the unit weight of concrete as zero, the maximum thermal stress is calculated as [2019, Set-I]
(a) Lα(T_t - T_b)
(b) Eα(T_t - T_b)
(c)
(d) Zero
Ans: (d)
Due to frictionless, thermal stress developed in concrete pavement slab is zero σ_th= 0

Q11: An element is subjected to biaxial normal tensile strains of 0.0030 and 0.0020. The normal strain in the plane of maximum shear strain is  [2019, Set-I]
(a) Zero 
(b) 0.001 
(c) 0.0025 
(d) 0.005
Ans: (c)
ε_x = 0.0030 
ε_y = 0.0020 
Normal strain in the plane of maximum shear strain


Q12: A plate in equilibrium is subjected to uniform stresses along its edges with magnitude σ_xx = 30 MPa and σ_yy = 50 MPa as shown in the figure.
The Young’s modulus of the material is 2 x 10¹¹ N/m² and the Poisson’s ratio is 0.3. If σ_zz is negligibly small and assumed to be zero, then the strain ε_zz is _________.  [2018 : 2 Marks, Set-I]
(a) -120 x 10^-6
(b) -60 x 10^-6 
(c) 0.0
(d) 120 x 10^-6
Ans:

So the answer is (d).

Q13: A 2 m long, axially loaded mild steel rod of 8 mm diameter exhibits the load-displacement (P-δ) behaviour as shown in the figure.
Assume the yield stress of steel as 250 MPa. The complementary strain energy (in N-mm) stored in the bar up to its linear elastic behaviour will be ________.  [2017 : 2 Marks, Set-II]
Ans:
Elastic strain: 

Note: For linear elastic material both complementary energy and strain energy is the same.

OR

By considering the given graph in question, between Axial Load and Displacement, the solution will be as follows:
Complementary stain energy:

It means there seems some error in the given data.

Q14: In a material under a state of plane strain, a 10 x 10 mm square centred at a point gets deformed as shown in the figure.
If the shear strain γ_xy at this point is expressed as 0.001 k (in rad), the value of k is _________.  [2017 : 1 Mark, Set-II]
(a) 0.50
(b) 0.25
(c) -0.25
(d) -0.50 
Ans: (d)
According to the sign convention:
In question, since angle has been increased, therefore, shear strain should be negative.


Q15: Consider the stepped bar made with a linear elastic material and subjected to an axial load of 1 kN, as shown in the figure.
Segments 1 and 2 have a cross-sectional area of 100 mm² and 60 mm². Young’s modulus of 2 x 10⁵ MPa and 3 x 10⁵ MPa, and length of 400 mm and 900 mm, respectively. The strain energy (in N-mm up to one decimal place) in the bar due to the axial load is _________.   [2017 : 2 Marks, Set-I]
Ans:

Question for Past Year Questions: Properties of Metals, Stress & Strain

Try yourself:An elastic isotropic body is in a hydrostatic state of stress as shown in the figure. For no change in the volume to occur, what should be its Poisson’s ratio?
[2016 : 2 Marks, Set-II]

• A.

  0.00
• B.

  0.25
• C.

  0.50
• D.

  1.00

Explanation

Volumetric strain:

⇒ 
As ΔV = 0

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Q16: A tapered circular rod of diameter varying from 20 mm to 10 mm is connected to another uniform circular rod of diameter 10 mm as shown in the following figure. Both bars are made of the same material with the modulus of elasticity, E = 2 x 10⁵ MPa. When subjected to a load P = 30πkN, the deflection at point A is ___ mm.  [2015 : 2 Marks, Set-I]
Ans:
Total elongation,
AB is uniform

BC is tapered


= (9 + 6) mm = 15 mm

Q17: For the state of stresses (in MPa) shown in the figure below, the maximum shear stress (in MPa) is _______.
[2014 : 2 Marks, Set-II]
Ans:

= 5.0 MPa

Question for Past Year Questions: Properties of Metals, Stress & Strain

Try yourself:The values of axial stress (σ) in kN/m², bending moment (M) in kNm, and shear force (V) in kN acting at point P for the arrangement shown in the figure are respectively.    
[2014 : 2 Marks, Set-II]

• A.

  1000, 75 and 25
• B.

  1250, 150 and 50
• C.

  1500, 225 and 75
• D.

  1750, 300 and 100

Explanation

Loading after removing the cable.


Bending moment = 50 x 3 = 150 kNm
Shear force = 50kN

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Question for Past Year Questions: Properties of Metals, Stress & Strain

Try yourself:A box of weight 100 kN shown in the figure is to be lifted without swinging. If all forces are coplanar, the magnitude and direction (θ) of the force (F) with respect to x-axis should be    [2014 : 2 Marks, Set-I]

• A.

  F = 56.389 kN and θ = 28.28º
• B.

  F = - 56.389 kN and θ = - 28.28º
• C.

  F = 9.055 kN and θ = 1.414º
• D.

  F = - 9.055 kN and θ = - 1.414º

Explanation

For no swinging force should be balanced, i.e.,

or


Dividing eq. (ii) by eq. (i) we get


Substituting


or

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Question for Past Year Questions: Properties of Metals, Stress & Strain

Try yourself:A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'K) at points T and ‘2’, and an inclined load acts at ‘2’, as shown.

If the load Pequals 100 kN, which of the following options represents forces P₁ and P₂ in the springs at points ‘1’ and ‘27'? 
[2011 : 2 Marks]

• A.

  R₁ = 20 kN and R₂ = 40 kN
• B.

  R₁ = 50 kN and R₂ = 50 kN
• C.

  R₁ = 30 kN and R₂ = 60 kN
• D.

  R₁ = 40 kN and R₂ = 80 kN

Explanation

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Question for Past Year Questions: Properties of Metals, Stress & Strain

Try yourself: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of 'K) at points T and ‘2’, and an inclined load acts at ‘2’, as shown.

Which of the following options represents the deflections δ₁ and δ₂ at points ‘Y and ‘2’?  [2011 : 2 Marks]

• A.

  
• B.

  
• C.

  
• D.

  

Explanation

The free diagram of the beam is shown below:

From similar triangles, we get:

⇒  ...(i)
Taking moments about hinge, we get:

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