GATE CE topic:solid-mechanics PYQs & Answers — Page 2

Questions 11–20 of 61. Imported answers require independent review unless marked reviewed.

The three-dimensional state of stress at a point is given by

The maximum shear stress at the point is

Your answerChoose one option.

20 MPa

15 MPa

5 MPa

25 MPa

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For a thin-walled section shown in the figure, points P, Q, and R are located on the major bending axis X − X of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange.

Diagram for Civil Engineering question 18

Qualitatively, the shear center of the section lies at

Your answerChoose one option.

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The steel angle section shown in the figure has elastic section modulus of 150.92 cm³ about the horizontal X – X axis, which passes through the centroid of the section.

The shape factor of the section is ______ (rounded off to 2 decimal places).

Diagram for Civil Engineering question 33

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Find the correct match between the plane stress states and the Mohr’s circles.

Plane stress states P, Q, R and S and Mohr’s circles I, II, III and IV are shown in the figures.

Diagram for Civil Engineering question 38

Your answerChoose one option.

(P)-(III); (Q)-(IV); (R)-(I); (S)-(II)

(P)-(III); (Q)-(II); (R)-(I); (S)-(IV)

(P)-(I); (Q)-(IV); (R)-(III); (S)-(II)

(P)-(I); (Q)-(II); (R)-(III); (S)-(IV)

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A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio (l/r) of 105, where l 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 0.5l 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

Your answerChoose one option.

28 °C

85 °C

400 °C

250 °C

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A homogeneous shaft PQ with fixed supports at both ends is subjected to a torsional moment T at point Q, as shown in the figure.

Diagram for Civil Engineering question 40

The polar moments of inertia of the portions PQ and QR of the shaft with circular cross-sections are

and

, respectively. The torsional moment reactions at the supports P and R are

and

, respectively.

and

, the ratio of the lengths

Your answerChoose one option.

0.50

0.25

4.00

2.00

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A hanger is made of two bars of different sizes. Each bar has a square cross-section. The hanger is loaded by three-point loads in the mid vertical plane as shown in the figure. Ignore the self-weight of the hanger. What is the maximum tensile stress in N/mm² anywhere in the hanger without considering stress concentration effects?

Diagram for Civil Engineering question 12

Your answerChoose one option.

15.0

25.0

35.0

45.0

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A circular solid shaft of span L = 5 m is fixed at one end and free at the other end. A torque T = 100 kN.m is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as G and J, respectively. The torsional rigidity GJ is 50,000 kN.m²/rad. The following are reported for this shaft:

Statement i) The rotation at the free end is 0.01 rad Statement ii) The torsional strain energy is 1.0 kN.m

With reference to the above statements, which of the following is true?

Your answerChoose one option.

Both the statements are correct

Statement i) is correct, but Statement ii) is wrong

Statement i) is wrong, but Statement ii) is correct

Both the statements are wrong

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When a simply-supported elastic beam of span L and flexural rigidity EI (E is the modulus of elasticity and I is the moment of inertia of the section) is loaded with a uniformly distributed load w per unit length, the deflection at the mid-span is

If the load on one half of the span is now removed, the mid-span deflection ______.

Your answerChoose one option.

reduces to Δ₀/2

reduces to a value less than Δ₀/2

reduces to a value greater than Δ₀/2

remains unchanged at Δ₀

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In a two-dimensional stress analysis, the state of stress at a point is shown in the figure. The values of length of PQ, QR, and RP are 4, 3, and 5 units, respectively. The principal stresses are ________. (round off to one decimal place)

Diagram for Civil Engineering question 39

Your answerChoose one option.

MPa,

MPa

MPa,

MPa

MPa,

MPa

MPa,

MPa

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GATE CE topic:solid-mechanics PYQs

Question 14

Question 18

Question 33

Question 38

Question 39

Question 40

Question 12

Question 14

Question 16

Question 39