The adjoining figure shows a schematic representation of a steel plate girder to be used as a simply supported beam with a concentrated load. For stiffeners PQ (running along the beam axis) and RS (running between the top and bottom flanges), which of the following pairs of statements will be TRUE?

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

Which of the following options represents the deflections ^$\delta_1$ and ^$\delta_2$ at points ‘1’ and ‘2’?

Directions: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’, and an inclined load acts at ‘2’, as shown.

If the load P equals 100 kN, which of the following options represents forces R₁ and R₂ in the springs at points ‘1’ and ‘2’?

For the simply supported beam of length L, subjected to a uniformly distributed moment M kN-m per unit length as shown in the figure, the bending moment (in kN-m) at the mid-span of the beam is

A three-hinged parabolic arch having a span of 20 m and a rise of 5 m carries a point load of 10 kN at quarter span from the left end as shown in the figure. The resultant reaction at the left support and its inclination with the horizontal are respectively

A disc of radius r has a hole of radius ^{$\frac{r}{2}$} cut out as shown. The centroid of the remaining disc (shaded portion) at a radial distance from the centre “O” is

A rigid bar GH of length L is supported by a hinge and a spring of stiffness K as shown in the figure below. The buckling load (P_cr) for the bar will be

The maximum shear stress in a solid shaft of circular cross section having diameter subjected to a torque T is $\tau$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

Cross section of a column consisting of two steel strips, each of thickness t and width b is shown in the figure below. The critical loads of the column with perfect bond and without bond between the strips are P and P₀ respectively. The ratio P/P_o is

The degree of static indeterminacy of a rigidly jointed frame in a horizontal plane and subjected to vertical loads only, as shown in figure below is

Consider the following statements. I. On a principal plane, only normal stress acts. II. On a principal plane, both normal and shear stresses act. III. On a principal plane, only shear stress acts. IV. Isotropic state of stress is independent of frame of reference. The TRUE statement(s) is/are

A hollow circular shaft has an outer diameter of 100 mm and a wall thickness of 25 mm. The allowable shear stress in the shaft is 125 MPa. The maximum torque the shaft can transmit is

Group I gives the shear force diagrams and Group II gives the diagrams of beams with supports and loading. Match the Group I with Group II. Group I

Group II

Direction: In the cantilever beam PQR shown in the figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity.

The deflection of the beam at ‘R’ is

Direction: In the cantilever beam PQR shown in the figure below, the segment PQ has flexural rigidity EI and the segment QR has infinite flexural rigidity.

The deflection and slope of the beam at ‘Q’ are respectively

Considering beam as axially rigid, the degree of freedom of a plane frame shown below is

Consider the beam AB shown in the figure below. Part AC of the beam is rigid while Part CB has the flexural rigidity EI. Identify the correct combination of deflection at end B and bending moment.

A simply supported beam AB has the bending moment diagram as shown in the following figure. The beam is possibly under the action of following loads :

A beam with the cross-section given below is subjected to a positive bending moment (causing compression at the top) of 16 kN-m acting around the horizontal axis. The tensile force acting on the hatched area of the cross-section is

The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions

For a linear elastic frame, if stiffness matrix is doubled, the existing stiffness matrix, the deflection of the resulting frame will be

A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce ‘pure shear’ state of stress in the wall of the cylinder, F should be equal to