# GATE Questions & Answers of Structural Analysis Civil Engineering

#### Structural Analysis 33 Question(s) | Weightage 06 (Marks)

The figure shows a simply supported beam PQ of uniform flexural rigidity EI carrying two moments M and 2M.

The slope at P will be

Consider the deformable pin-jointed truss with loading, geometry and section properties as shown in the figure.

Given that $\style{font-family:'Times New Roman'}{E=2\times10^{11}\;\mathrm N/\mathrm m^2,\;A=10\;\mathrm{mm}^2\;,\;L=1\;\mathrm m\;\mathrm{and}\;P=1\mathrm{kN}}$ The horizontal displacement of Joint C (in mm, up to one decimal place) is ______

All the members of the planar truss (see figure), have the same properties in terms of area of cross-section $(A)$ and modulus of elasticity $(E)$.

For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the truss is:

A prismatic beam P-Q-R of flexural rigidity $EI=1\times10^4$ kNm2 is subjected to a moment of 180 kNm at Q as shown in the figure.

The rotation at Q (in rad, up to two decimal places) is ______

The figure shows a two-hinged  parabolic arch of spam L subjected to uniformly distributed load of  intensity  q per unit length

The maximum bending moment  in the arch is qual to

A planar truss tower structure is shown in the figure.

Consider the following statement about the external and internal deteriminacies of the truss.

(P) Externally Determinate
(Q) External static Indeterminancy = 1
(R) External static Indeterminancy = 2
(S) Internally Determinate
(T) Internal static Indeterminancy = 1
(U) Internal static Indeterminancy = 2

Which one of the following option is correct?

Consider the beam ABCD shown in the figure.

For a moving concentraed load of 50kN on the magnitude of the maximum bending moment (in kN-m) obtained at the support C will be equal  to ____________

Consider the frame shown in the figure:

If the axial and shear deformations in diferent members of the frame are assumed to be negligible, the reduction in the degree of kinematical indeterminacy would be equal to

Consider the plane truss with load P as shown in the figure. Let the horizontal and vertical reactions at the joint B be HB and VB, respectively and VC be the vertical reaction at the joint C.

Which one of the following sets gives the correct values of VB, HB and VC?

A 3 m long simply supported beam of uniform cross section is subjected to a uniformly distributed load of w = 20 kN/m in the central 1 m as shown in the figure.

If the flexural rigidity (EI) of the beam is 30 x 106 N-m2, the maximum slope (expressed in radians) of the deformed beam is

Two beams PQ (fixed at P and with a roller support at Q, as shown in Figure I, which allows vertical movement) and XZ (with a hinge at Y) are shown in the Figures I and II respectively. The spans of PQ and XZ are L and 2L respectively. Both the beams are under the action of uniformly distributed load (W) and have the same flexural stiffness, EI (where, E and I respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be ${\mathrm\delta}_{\max1}$ and ${\mathrm\theta}_{\max1}$ respectively, in the case of beam PQ and the corresponding quantities for the beam XZ be ${\mathrm\delta}_{\max2}$ and ${\mathrm\theta}_{\max2}$ respectively.

Which one of the following relationships is true?

A plane truss with applied loads is shown in the figure.

The members which do not carry any force are

The kinematic indeterminacy of the plane truss shown in the figure is

The portal frame shown in the figure is subjected to a uniformly distributed vertical load w (per unit length).

The bending moment in the beam at the joint ‘Q’ is

For the 2D truss with the applied loads shown below, the strain energy in the member XY is _______ kN-m. For member XY, assume AE=30 kN, where A is crosssection area and E is the modulus of elasticity.

A guided support as shown in the figure below is represented by three springs (horizontal, vertical and rotational) with stiffness $kx,ky$ and $k_\theta$ respectively. The limiting values of $kx,ky$ and $k_\theta$ are :

A simply supported beam AB of span, L = 24 m is subjected to two wheel loads acting at a distance, d = 5 m apart as shown in the figure below. Each wheel transmits a load, P = 3 kN and may occupy any position along the beam . If the beam is an I-section having section modulus, S = 16.2 cm3, the maximum bending stress (in GPa) due to the wheel loads is_____________.

The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is

In a beam of length L, four possible influence line diagrams for shear force at a section located at a distance of $\frac{L}{4}$ from the left end support (marked as P, Q, R and S) are shown below. The correct influence line diagram is

For the cantilever beam of span 3 m (shown below), a concentrated load of 20 kN applied at the free end causes a vertical displacement of 2 mm at a section located at a distance of 1 m from the fixed end. If a concentrated vertically downward load of 10 kN is applied at the section located at a distance of 1 m from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in mm) is __________

For the truss shown below, the member PQ is short by 3 mm. The magnitude of vertical displacement of joint R (in mm) is _______________

The static indeterminacy of the two-span continuous beam with an internal hinge, shown below, is ______________

The pin-jointed 2-D truss is loaded with a horizontal force of 15 KN at joint S and another 15 KN vertical force at joint U, as shown.Find the force in member RS (in KN) and report your answer taking tension as positive and compression as negative. __________

A uniform beam weighing 1800N is supported  at E and F by cable ABCD. Determine the tension(in N) in segment AB of this cable (correct to 1-decimal place). Assume the cables ABCD,BE and CF to be weightless.____________

Beam PQRS has internal hinges in spans PQ and RS as shown. The beammay be subjeted to a moving distributed vertical load of maximum intensity 4 kN/m of any length anywhere on the beam. The maximum absolute value of the shear force (in KN) that can occur due to this loading just to the right of support Q shall be:

For the truss shown in the figure, the force in the member QR 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

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

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, Pcr for the bar will be

The degree of static indeterminacy of the rigid frame having two internal hinges as shown in the figure below, is

The members EJ and IJ of a steel truss shown in the figure below are subjected to a temperature rise of 30oC. The coefficient of thermal expansion of steel is 0.000012 per oC per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of truss, is