GATE CE Solid Mechanics : National Champion Test for ESE & GATE CE Exams

Question 1

A steel section is subjected to a combination of shear and bending actions. The applied shear force is V and the shear capacity of the section is V_s. For such a section, high shear force (as per IS : 800–2007) is defined as

Question 2

The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force P and a moment M at mid–height. The reaction (s) at R is/are

Question 3

The possible location of shear centre of the channel section, shown below, is

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Question 4

The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to

Question 5

The ‘plane section remains plane’ assumption in bending theory implies:

Question 6

A circular solid shaft of span L = 5 m is fixe at one end and free at the other end. A twisting moment T = 100 kN–m is applied at the free end. The torsional rigidity GJ is 50000 kN–m²/red.
Following statements are made for this shaft
(I) The maximum rotation is 0.01 rad
(II) The torsional strain energy is 1 kN–m
With reference to the above statements, which of the following applies?

Question 7

A solid circular shaft of diameter d and length L is fixed at one end and free at the other end. A torque T is applied at the free end. The shear modulus of the material is G. The angle of twist at the free end is

Question 8

A solid circular shaft subjected to a torque T produces maximum shear stress f_s, which is the maximum principal value in the material. The corresponding diameter of the shaft should be

Question 9

A circular column of external diameter D, and internal diameter d, carries an eccentric load such that tension is developed nowhere. What shall be the diameter of the core?

Question 10

The value of modulus of elasticity for a material is 200 GN/m² and Poisson’s ratio is 0.25. What is its modulus of rigidity?

Question 11

A cantilever beam of T cross-section carries uniform distributed load where does the maximum magnitude of the bending stress occur?

Question 12

A square section as shown in the figure below is subjected to bending moment M.

What is the maximum bending stress?

Question 13

A simply supported beam has uniform cross-section, b=100 mm, d=200 mm, throughout its length. The beam is subjected to a maximum bending moment 6

10⁷ N-mm. The corresponding bending stress developed in the beam is

Question 14

Which one of following is the reaction of the cantilever at B as shown in the figure below?

Question 15

The limit of proportionality in the material of a structural steel member, when subjected to simple tension, is 280 N/mm². The principal stresses in the member are

(Tensile) and

(Compressive μ= 0.3. According to maximum strain theory, the factor of safety is

Question 16

Consider the following statements:
If the planes at right angles carry only shearstress of magnitude q in a certain instance, then the
1) diameter of Mohr's circle would be equal to 2q.
2) centre of Mohr's circle would lie at the origin
3) principal stresses are unlike and are of magnitude q each
4) angle between the principal plane and the plane of maximum shear would be 45 °
Which of the above statements are correct?

Question 17

A beam of square cross-section is placed such that its neutral axis coincides with its diagonal and it is subjected to a shear force F. What is the ratio of the maximum shear stress to the shear stress at the neutral axis?

Question 18

For the beam-system as shown, if the deflection at C is zero, then the ratio

is

Question 19

A 20 cm lon g rod of uniform rectangular section 8 mm wide

1.2 mm thick is bent into the form of a circular arc resulting in a central displacement of 0.8cm. Neglecting second-order quantities in computations, what is the longitudinal surface strain (approximate ) in the rod?

Question 20

A thin cylinder of thickness ‘t’ width ‘b’ and internal radius ‘r’ is subjected to a pressure ‘p’ on the entire internal surface. What is the change in radius of the cylinder ? (

is the Poisson’s ratio and E is the modulus of elasticity) ?

Question 21

A bar of circular cross-section of diameter D is subjected to a torque T at B as shown in the figure given below

What is the angle of twist at A?

Question 22

The part of the shear force diagram for a beam is shown in the figure
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If the bending moment at B is -9kN m, then the bending moment at C is

Question 23

Match List-1 (Cantilever loading) with List-II (shear Force Diagram) and select the correct answer using the coded given below the lists:
Lists-I
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List-II
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Question 24

Fracture Difficultness is measured in terms of

Question 25

Consider the Mohr’s circle show below:
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What is the state of stress represented by this circle?

Question 26

In a strained material, normal stresses on two mutually perpendicular planes are σ_x and σ_y (both alike) accompanied by a shear stress τ_xy. One of the principal stresses will be zero, only when __________.

Question 27

In a tensile test, near the elastic limit zone

Question 28

A structural member subjected to an axial compressive is called

Question 29

What is the slenderness ratio of a 4 m long column with fixed ends if its cross section is square of side 40 mm?

Question 30

A T-section beam is simply supported and subjected to a uniformity load over its whole span. Maximum longitudinal stress in the beam occurs at