Engineering Sciences
GATE XE Mechanics of deformable bodies PYQs
Build your understanding with focused practice from past exam papers.
Questions 41–50 of 133. Imported answers require independent review unless marked reviewed.
Question 70
Open questionXE-DMCQ1 markNeeds review
A thin walled, closed cylindrical vessel of inside diameter
and wall thickness
contains a fluid under pressure
. The figure below shows a part of the cylindrical vessel; end caps are not shown. Consider the small element shown with sides parallel and perpendicular to the axis of the cylinder. The stresses
and
are
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Open questionXE-DNAT1 markNeeds review
A simply supported beam of length 3 m is loaded as shown in the figure.
The magnitude of the shear force (in kN) at the mid-point of the beam is______(rounded off to one decimal place).
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Open questionXE-DNAT1 markNeeds review
For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is______(rounded off to one decimal place).
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Open questionXE-DMCQ2 marksNeeds review
A cylinder made of rubber (length = L and diameter = d) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is E and its Poisson’s ratio is
. The cylinder is subjected to a small uniform pressure
as shown in the figure. The resulting axial strain (
) is
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Open questionXE-DMCQ2 marksNeeds review
The state of stress at the critical location in a structure is
,
,
. The yield stress for the material in uniaxial tension is 400 MPa. Select the correct statement among the following.Your answerChoose one option.
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Open questionXE-DMCQ2 marksNeeds review
The figure shows a column of rectangular cross section 100 mm × 80 mm. It carries a load of 60 kN at a point 30 mm from the edge P Q. The values of stress component
on surfaces
and
, at points far away from both ends of the column, are respectively 
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Open questionXE-DMCQ2 marksNeeds review
Consider an electric pole with dimensions as shown in the figure. Let the end R be subjected to a vertical force F. The flexural rigidity of both vertical and horizontal bars is EI. Neglect the axial deflection of the vertical bar, and all effects of self-weight. The vertical deflection at end R is
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Open questionXE-DMSQ2 marksNeeds review
A uniform cantilever beam has flexural rigidity EI and length L. It is subjected to a concentrated force F and moment M = 2FL at the free end as shown. The deflection (δ) at the free end is
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Open questionXE-DNAT2 marksNeeds review
A thin steel plate is loaded in the x-y plane as shown in the figure. Take the Poisson’s ratio of steel to be 0.3 and the modulus of elasticity of steel to be 200 GPa. The strain along the z-direction is
. The value of
(in MPa) is_____(rounded off to one decimal place). 
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Open questionXE-DNAT2 marksNeeds review
A composite rod made of steel and copper is fixed immovably at its ends as shown in the figure. The length of each portion of the rod is 1 m as shown. The cross-section of both portions are the same. The modulus of elasticity of steel and copper are 200 GPa and 100 GPa, respectively. The coefficients of thermal expansion of steel and copper are 12 × 10
/°C and 18 × 10
/°C, respectively. The composite rod is initially stress free. Then, the temperature of the composite rod is increased by 100 °C. The magnitude of axial stress (in MPa) developed in the steel rod is_____(rounded off to one decimal place). 
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