Mechanical and structural analysis miscellaneous

Mechanical and structural analysis miscellaneous

Easy Questions

Mechanics and Structural Analysis

Mechanical and structural analysis miscellaneous
  1. Carry-over factor CAB for the beam shown in the figure below is








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    There is no role for internal hinge in carry over factor

    Correct Option: D

    There is no role for internal hinge in carry over factor

  1. Consider the beam ABCD and the influence line as shown below. The influence it pertains to








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    By muller Breslaw principle.

    Correct Option: B

    By muller Breslaw principle.

  1. Vertical reaction developed at B in the frame below due to the applied load of 100 kN (with 150,000 mm2 cross-sectional area and 3.125 × 109 mm2 moment of inertia for both members) is








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    Due to load P, the member AC undergo compression
    Let the reaction at C = R
    Thus the remaining vertical force is 100 – R. It is taken up by AB at B
    Deflection at A along AC = deflection at A for cantilever AB.

    ⇒
    RL
    		=
    (100 - R)L3
    AE3EI

    R × 1000
    		=
    (100 - R)10003
    150000 × E3 × 3.125 × 109

    100 - R
    		=
    1000 × 3 × 3.125 × 109
    R10003 × 150000

    ∴ R = 94.1 kN
    ∴ Reaction at B = 100 – R = 5.9 kN

    Correct Option: A

    Due to load P, the member AC undergo compression
    Let the reaction at C = R
    Thus the remaining vertical force is 100 – R. It is taken up by AB at B
    Deflection at A along AC = deflection at A for cantilever AB.

    ⇒
    RL
    		=
    (100 - R)L3
    AE3EI

    R × 1000
    		=
    (100 - R)10003
    150000 × E3 × 3.125 × 109

    100 - R
    		=
    1000 × 3 × 3.125 × 109
    R10003 × 150000

    ∴ R = 94.1 kN
    ∴ Reaction at B = 100 – R = 5.9 kN

  1. 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








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    Consider a thin long cylindrical tank
    2σ × t × l = p.2r.l

    ∴ σ0 =
    pr
    		 (tensile)
    t

    Due to pressure at longitudinal section
    πr2 × p = 2πrt × σz
    σz =
    pr
    2t

    Due to compressive force, F
    Longitudinal force =
    F
    2πrt

    ∴ Total longitudinal stress
    =
    pr
    		-
    F
    		(compressive)
    2t2πrt

    τ =
    σ1 - σ2
    2

    ⇒
    pr
    		= -
    pr
    		-
    F
    t2t2πrt

    ⇒
    F
    		=
    3pr
    2πrt2t

    ⇒ F = 3πpr2

    Correct Option: C

    Consider a thin long cylindrical tank
    2σ × t × l = p.2r.l

    ∴ σ0 =
    pr
    		 (tensile)
    t

    Due to pressure at longitudinal section
    πr2 × p = 2πrt × σz
    σz =
    pr
    2t

    Due to compressive force, F
    Longitudinal force =
    F
    2πrt

    ∴ Total longitudinal stress
    =
    pr
    		-
    F
    		(compressive)
    2t2πrt

    τ =
    σ1 - σ2
    2

    ⇒
    pr
    		= -
    pr
    		-
    F
    t2t2πrt

    ⇒
    F
    		=
    3pr
    2πrt2t

    ⇒ F = 3πpr2

  1. 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








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    Variation of shear stress,

    τ =
    V.Ay
    lb

    Taking a height y from N. A.

    Correct Option: B

    Variation of shear stress,

    τ =
    V.Ay
    lb

    Taking a height y from N. A.