Questions Revised

1. A three hinged arch shown in Figure is quarter of a circle. If the vertical and horizontal components of reaction at A are equal. The value of θ is (GATE 1998)

(a) 600 (b) 450 (c) 30° (d) None in (0°, 90°)

2. Figure below shows a cantilever member bent in the form of a quadrant of a circle with a radius of 1.0 m up to the centre of the cross section. The member is subjected a load of 2 kN as shown. The member is having circular cross section with a diameter of 50 mm. Modulus of elasticity (E) of the material is 2.0 x 105 MPa. Calculate the horizontal displacement of the tip.

(GATE 1999)

3. The dimensions of the flexural rigidity of a beam element in mass(M), length(L), and time(T) is given by (GATE 2000)(A) MT-2 (B) ML3T-2 (C) ML-1T2 (D) ML-1T-2

4. The stress-strain diagram for 2 materials A and B is shown below: (GATE 2000)

The following statements are made based on this diagram:(I) Material A is more brittle than material 3.(II) The ultimate strength of material B is more than that of AWith reference to the above statements, which of the following applies?

(A) Both the statements are false. (B) Both the statements are true.(C) I is true but II is false. (D) I is false but II is true.

5. A simply supported beam with an overhang is traversed by a unit concentrated moment from the left to the right as shown below: (GATE 2000)

The influence line for reaction at B is given by

6. The following two statements are made with reference to the planar truss shown below:

I. The truss is statically determinateII. The truss is kinematically determinate

With reference to the above statements, which of the following applies? (GATE 2000)(A) Both statements are true. (B) Both statements are false.(C) II is true but I is false. (D) I is true but II is false.

7. Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise Δt in the bar BD alone in the plane truss shown below: (GATE 2001)

(A) No reactions develop at supports A and D.(B) The bar BD will be subject to a tensile force.(C) The bar AC will be subject to a compressive force.(D) The bar BC will be subject to a tensile force.

8. Identity the FALSE statement from the following, pertaining to the methods of structural analysis. (GATE 2001)(A) Influence lines for stress resultants in beams can be drawn using Muller Breslau’s Principle.(B) The Moment Distribution Method is a force method of analysis, not a displacement method.(C) The Principle of Virtual Displacements can be used to establish a condition of equilibrium.(D) The Substitute Frame Method is not applicable to frames subjects to significant sidesway.

9. The figure below shows a cable-supported cantilever beam of span L subject to a concentrated load P at mid-span. (GATE 2001)(a) Express the bending moment M(x) at any section of the beam AB located at a distance x from the fixed end A, in terms of P, Land the cable tension T.(b) Applying the Theorem of Least Work, derive an expression for T in terms of P; assuming

EA=√3 El

L2 Consider only the flexural strain energy in the beam and the axial strain energy in

the cable.

10. Muller Breslau principle in structural analysis is used for (GATE 2003)(A) Drawing influence line diagram for any force function(B) Writing virtual work equation(C) Super-position of load effects(D) None of these

11. The effective length of a column in a reinforced concrete building frame, as per IS : 456-2000, is independent of the (GATE 2003)

(A) Frame type i.e., braced (no sway) or un-braced (with sway)(B) Span of the beam(C) Height of the column(D) Loads acting on the frame

12. A curved member with a straight vertical leg is carrying a vertical load at Z, as shown in the figure. The stress resultants in the XV segment are (GATE 2003)

(A) Bending moment, shear force and axial force (B) Bending moment and axial force only(C) Bending moment and shear force only (D) Axial force only

13. An “H” shaped frame of uniform flexural rigidity EI is loaded as shown in the figure. The relative outward displacement between points K and O is (GATE 2003)

(A) RLh2

EI(B) Rh L

2

EI(C) RLh

2

3 EI(D)

RLh3 EI

14. A simply supported beam of uniform rectangular cross-section of width b and depth h is subjected to linear temperature gradient, 0° at the top and T° at the bottom, as shown in the figure. The coefficient of linear expansion of the beam material is α. The resulting vertical deflection at the mid- span of the beam is (GATE 2003)

(A) αT h2

8 Lupward (B) αT L

2

8Lupward (C) αT h

2

8 Ldownward (D) αT L

2

8Ldownward

15. Group 1 shows different loads acting on a beam and Group 2 shows different bending moment distributions. Match the toad with the corresponding bending moment diagram.

(GATE 2003)

Codes:

P Q R S(A) 4 2 1 3(B) 5 4 1 3(C) 2 5 3 1(D) 2 4 1 3

16. For the plane truss shown in the Figure. The number of zero force members for the given loading is (GATE 2004)

(a) 4 (b) 8 (c) 11° (d) 13

17. For linear elastic systems, the type of displacement function (or the strain energy is(A) linear (B) quadratic (C) cubic (D) quartic (GATE 2004)

18. For a linear elastic structural system, minimization of potential energy yields(A) Compatibility conditions (B) Constitutive relations(C) Equilibrium equations (D) Strain-displacement relations (GATE 2004)

19. A homogeneous, simply supported prismatic beam of width B, depth D and span L is subjected to a concentrated load of magnitude P. The load can be placed anywhere along the span of the beam. The maximum flexural stress developed in beam (GATE 2004)

(A) 23PL

B D2 (B) 34PL

B D2 (C) 43PL

B D2 (D) 32PL

B D2

20. In a two dimensional stress analysis, the state of stress at a point is shown below. If s = 120 MPa and t = 70 MPa, then sx and sy are respectively (GATE 2004)

(A) 26.7 MPa and 172.5 MPa(B) 54 MPa and 128 MPa(C) 67.5 MPa and 213.3 MPa(D) l6 MPa and l38 Mpa

21. A circular solid shaft of span L =5 m is fixed 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. (GATE 2004)(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?(A) Both statements are true (B) Statement I is true but II is false(C) Statement It is true but I is false (D) Both the statements are false

22. The plane frame below is analyzed by neglecting axial deformations. Following statements are made with respect to the analysis (GATE 2004)

(I) Column AB carries axial force only(II) Vertical deflection at the center of beam BC is 1mm

With reference to the above statements, which of the following applies?

(A) Both the statements are true (B) Statement I is true but II is false(C) Statement II is true but I is false (D) Both the statements are false

23. Mohr’s circle for the state of stress defined by [30 00 30 ] MPa is a circle with

(GATE 2005)(A) center at (0. 0) and radius 30 MPa (B) center at (0, 0) and radius 60 MPa(C) center at (30, 0) and radius 30 MPa (D) center at (30,0) and zero radius

24. The buckling load P = Pcr for the column AB in the figure, as KT approaches infinity, become απ 2EIL2 where α as equal to (GATE 2005)

(A) 0.25 (B) 2.05 (C) 1.00 (D) 4.00

25. For the sect ion shown below, second moment of the area about an axis d/4 distance above the bottom of the area is (GATE 2005)

(A) bd3

48(B) bd

3

12(C) 7bd

3

48(D)

bd3

3

26. 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 (GATE 2005)

(A) 0 (B) 5.9 kN (C) 8.9 kN (D) 17.8 kN

27. T-section of a beam is formed by gluing wooden planks as shown in the figure below. If this beam transmits a constant vertical shear force of 3000 N, the glue at any of the four joints will be subjected to a shear force (in kN per meter length) of (GATE 2005)

(A) 3.0 (B) 4.2 (C) 8.0 (D) 10.7

28. If a beam of rectangular cross-section is subjected to a vertical shear force V. the shear force carried by the upper one-third of the cross-section is (GATE 2005)

(A) 0 (B) 7V27

(C) 8V27

(D) V3

29. Consider the beam ABCD and the influence line as shown below. The influence line pertains to (GATE 2005)

(A) reaction at A, RA (B) shear force at B, VB

(C) shear force on the left of C, VC- (D) shear force on the right of C, VC

+

30. An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (GATE 2007)(A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa

31. A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (GATE 2007)(A) 200kN (B) 283kN (C) 400kN (D) 800kN

32. The stiffness coefficient kij indicates (GATE 2007)

(A) force at i due to a unit deformation at j.(B) deformation at j due to a unit force at i.(C) deformation at i due to a unit force at j.(D) force at j due to a unit deformation at i.

33. For an isotropic material, the relationship between the Young’s modulus (E),shear modulus (G) and Poisson’s ratio (μ) is given by (GATE 2007)

(A) G= E2(1+μ) (B) E= G

2(1+μ) (C) E= G(1+2μ) (D) G= E

2(1−μ)

34. A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by 100C. If the coefficient of thermal expansion is 12 x 10-6 per ◦C and the Young’s modulus is 2 x 105 MPa, the stress in the bar is (GATE 2007)(A) zero (B) 12MPa (C) 24MPa (D) 2400MPa

35. A rigid bar is suspended by three rods made of the same material as shown in the figure. The area and length of the central rod are 3A and L, respectively while that of the two outer rods are 2A and 2L respectively. If a downward force of 50kN is applied to the rigid bar, the forces in the central and each of the outer rods will be (GATE 2007)(A) 16.67 kN each (B) 30kN and 15kN(C) 30kN and 10kN (D) 21.4kN and 14.3kN

36. A mild steel specimen is under uni-axial tensile stress. Young’s modules and yield stress for mild steel are 2 x 105 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is (GATE 2008)(A) 156 Nmm/mm3 (B) 15.6 Nmm/mm3

(C) 1.56 Nmm/mm3 (D) 0.156 Nmm/mm3

37. 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 (GATE 2008)

(A) 0.5 KL (B) 0.8 KL (C) 1.0KL (D) 1.2KL

38. The members EJ and IJ of a steel truss shown in the figure below are subjected to a temperature rise of 300◦C. The coefficient of thermal expansion of steel is 0.000012 per ◦C per unit length. The displacement (mm) of joint E relative to joint H along the direction HE of truss, is (GATE 2008)

(A) 0.255 (B) 0.589 (C) 0.764 (D) 1.026

39. The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to a torque T is t. 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 (GATE 2008)

(A) 2 t (B) t (C) t /2 (D) t /4

40. The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are) (GATE 2008)

(A) PQ only (B) PQ and QR (C) QR and RS (D) PQ and RS

41. A vertical PQ of length L is fixed at its top end P and has a flange to the bottom end Q. A weight W is dropped vertically from a height h (<L) on to the flange. The axial stress in the rod can be reduced by (GATE 2008)(A) increasing the length of the rod(B) decreasing the length of the rod(C) decreasing the area of cross-section of the rod(D) increasing the modulus of elasticity of the material

42. The symmetry of stress tensor at a point in the body under equilibrium is obtained from (GATE 2005)

(A) Conservation of mass (B) Force equilibrium equations(C) Moment equilibrium equations (D) Conservation of energy

43. The components of strain tensor at a point in the plane strain case can be obtained by measuring longitudinal strain in following directions. (GATE 2005)(A) Along any two arbitrary directions(B) Along any three arbitrary directions(C) Along two mutually orthogonal directions(D) Along any arbitrary direction

44. Consider beam as axially rigid, the degree of freedom of a plane frame shown below is

(GATE 2005)(A) 9 (B) 8 (C) 7 (D) 6

45. For a linear elastic frame, if stiffness matrix is doubled, the existing stiffness matrix, the deflection of the resulting frame will be (GATE 2005)

(A) twice the existing value (B) half the existing value(C) the same as existing value (D) indeterminate value

46. A concrete beam of rectangular cross section of 200mm x40mm is pre-stressed with a force 400kN at eccentricity 100mm. the maximum compressive stress in the concrete is

(GATE 2005)(A) 12.5N/mm2 (B) 7.5 N/mm2 (C) 5.0 N/mm2 (D) 2.5 N/mm2

47. A circular shaft shown in the figure is subject to torsion T at two points A and B. The torsional rigidity of portions CA and BD is GJ1 and that of portion AB is GJ2. The rotations of shaft at points A and B are q1 and q2. The rotation q1 is (GATE 2005)

(A) TLE

GJ1+GJ 2(B)

TLGJ1

(C) TLGJ2

(D)

TLEGJ1−GJ2

48. If the principle stresses in a two-dimensional case are -10MPa and 20MPa respectively, then maximum shear stress at the point is (GATE 2005)(A) 10MPa (B) 15MPa (C) 20MPa (D) 30MPa

49. The bending Moment diagram for a beam is given below:

(GATE 2005)The shear force at sections aa’ and bb’ respectively are of the magnitude(A) 100kN, 150kN (B) zero, 100kN(C) zero, 50kN (D) 100kN, 100kN

50. Match the following:Group 1 (GATE 2005)P Slope deflection method Q Moment deflection methodR Method of three moments S Castigliano’s second theorem

Group 21 Force method

2 Deflection method(A) P-1, Q-2, R-1, S-2 (B) P-1, Q-1, R-2, S2(C) P-2, Q-2, R-1, S-1 (D) P-2, Q-1, R-2, S-1

51. All members of the frame shown below have the same flexural rigidity EI and length L. If a moment M is applied at joint B, the rotation of the joint is (GATE 2005)

(A) ML

12EI(B)

ML11EI

(C) ML8 EI

(D) ML7 EI

52. A truss is shown in the figure. Members are to equal cross section A and same modulus of elasticity E. A vertical force P is applied at point C. (GATE 2005)

(i) Force in the member AB of the truss is(A) P/√2 (B) P/√3 (C) P/2 (D) P

(ii) Deflection of the point C is

(GATE 2005)

(A) (2√2+1)

2LEA

(B) √ 2LEA

(C) (2√2+1) LEA

(D) (√2+1) LEA

53. The square root of the ratio of moment of inertia of the cross section to its cross sectional area is called (GATE 2009)(A) second moment of area (B) slenderness ratio(C) section modulus (D) radius of gyration

54. The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of the cross-section of the beam is called (GATE 2009)(A) Moment center (B) centroid (C) shear centre (D) elastic center

55. 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 (GATE 2009)

(A) 6 (B) 4 (C) 3 (D) 1

56. The number of independent elastic constants for a linear elastic isotropic and homogeneous material is (GATE 2010)(A) 4 (8) 3 (C) 2 (D) 1

57. For the cantilever bracket, PQRS, loaded as shown in the adjoining figure (PQ=RS=L and QR = 2L), which of the following statements is FALSE? (GATE 2011)

(A) The portion RS has a constant twisting moment with a value of 2WL.(B) The portion QR has a varying twisting moment with a maximum value of WL.(C) The portion PQ has a varying bending moment with a maximum value of WL.(D) The portion PQ has no twisting moment.

58. 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 (GATE 2012)(A) A vertical force equal to P(B) A vertical force equal to P/2(C) A vertical force equal to P and a horizontal force equal to M/h(D) A vertical force equal to P/2 and a horizontal force equal to M/h

59. Two steel columns P (length L and yield strength fy=250 MPa) and Q (length 2L and yield strength fy=500 MPa) have the same cross-sections and end-conditions. The ratio of buckling load of column P to that of column Q is: (GATE 2013)(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0

60. The state of 2D-stress at a point is given by the following matrix of stresses:

[σ xx σ xyσ xy σ yy ]=[100 30

30 20]MPa (GATE 2013)

What is the magnitude of maximum shear stress in MPa?(A) 50 (B) 75 (C) 100 (D) 110

61. Beam PQRS has internal hinges in spans PQ and RS as shown, The beam may be subjected 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 (GATE 2013)

(A) 30 (B) 40 (C) 45 (D) 55

62. A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown. (GATE 2013)

(i)If load P=80 kN, find the reaction R (in kN) (correct to 1-decimal place) using elastic analysis.______(ii)If the magnitude of load P is increased till collapse and the plastic moment carrying capacity of steel beam section is 90 kNm, determine reaction R(in kN)(correct to 1-decimal place) using plastic analysis. ______