Civil Engineering
GATE CE Solid Mechanics PYQs
Build your understanding with focused practice from past exam papers.
Questions 31–40 of 61. Imported answers require independent review unless marked reviewed.
Question 20
Open questionCENAT1 markNeeds review
The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle
, locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction. 
The absolute magnitude of the shear stress component
(in MPa, round off to one decimal place) in x-y coordinate system is ______.Log in to check the answer
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Open questionCENAT1 markNeeds review
The equation of deformation is derived to be
for a beam shown in the figure. 
The curvature of the beam at the mid-span (in units, in integer) will be ______.
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Open questionCENAT2 marksNeeds review
An elevated cylindrical water storage tank is shown in the figure. The tank has inner diameter of 1.5 m. It is supported on a solid steel circular column of diameter 75 mm and total height (L) of 4 m. Take, water density = 1000 kg/m³ and acceleration due to gravity = 10 m/s². If elastic modulus (E) of steel is 200 GPa, ignoring self-weight of the tank, for the supporting steel column to remain unbuckled, the maximum depth (h) of the water permissible (in m, round off to one decimal place) is
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Open questionCENAT2 marksNeeds review
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.
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
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Open questionCEMCQ1 markNeeds review
The state of stress represented by Mohr’s circle shown in the figure is
Your answerChoose one option.
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Open questionCEMCQ1 markNeeds review
In a two-dimensional stress analysis, the state of stress at a point
is
The necessary and sufficient condition for existence of the state of pure shear at the point
, isYour answerChoose one option.
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Open questionCEMCQ1 markNeeds review
A weightless cantilever beam of span
is loaded as shown in the figure. For the entire span of the beam, the material properties are identical and the cross section is rectangular with constant width.
From the flexure-critical perspective, the most economical longitudinal profile of the beam to carry the given loads among the options given below, is
Your answerChoose one option.
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Open questionCEMCQ2 marksNeeds review
A prismatic linearly elastic bar of length
, cross-sectional area
, and made up of a material with Young’s modulus
, is subjected to axial tensile force as shown in the figures 
. When the bar is subjected to axial tensile forces
and
, the strain energies stored in the bar are
and
, respectively.If
is the strain energy stored in the same bar when subjected to an axial tensile force
, the correct relationship isYour answerChoose one option.
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Open questionCENAT2 marksNeeds review
A rigid, uniform, weightless horizontal bar is connected to three vertical members P, Q and R as shown in the figure (not drawn to the scale).
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 load is applied, a gap of 2 mm exists 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 displaced by 5 mm in the vertically downward direction. The magnitude of the load W (in kN, round off to the nearest integer), is ____________.
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Open questionCENAT2 marksNeeds review
The flange and web plates of the doubly symmetric built-up section are connected by continuous 10 mm thick fillet welds as shown in the figure (not drawn to the scale). The moment of inertia of the section about its principal axis X–X is
. The permissible shear stress in the fillet welds is 100 N/mm
. The design shear strength of the section is governed by the capacity of the fillet welds. 
The maximum shear force (in kN, round off to one decimal place) that can be carried by the section, is _____.
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