Mechanical and structural analysis miscellaneous

Mechanical and structural analysis miscellaneous

Easy Questions

Mechanics and Structural Analysis

Mechanical and structural analysis miscellaneous
  1. In a beam of length L, four possible influence line diagrams for shear force at a section located at a distance of L/4 from the left end support (marked as P, Q, R and S) are shown below. The correct influence line diagram is








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    NA

    Correct Option: A

    NA

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








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    Degree of static indeterminacy,
    Ds = Dse + Dsi
    = (re – 3) + 3c – rr
    = (4 – 3) + (3 × 0) – 1 = 0

    Correct Option: A

    Degree of static indeterminacy,
    Ds = Dse + Dsi
    = (re – 3) + 3c – rr
    = (4 – 3) + (3 × 0) – 1 = 0

  1. The ultimate collapse load (P) in terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with P acting as its mid-span as shown in the figure, would be








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    By principle of virtual work
    - MP θ - MP θ - MP θ + P.(L/2)θ = 0
    - MP θ + P.(L/2)θ = 0

    P =
    6MP
    L

    Correct Option: C


    By principle of virtual work
    - MP θ - MP θ - MP θ + P.(L/2)θ = 0
    - MP θ + P.(L/2)θ = 0

    P =
    6MP
    L

  1. 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








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    When a cut is made just to the right of Q and displacements are given such that A'B' is parallel to B'C'. is very close at Q, displacement of B' to the left will be zero and that to the right will be, 1.

    Hence slope of B'C' = 1/20
    ⇒ Slope of B'A' = 1/20

    ⇒ Ordinate at A' =
    1
    		× 5 = 0.25
    20

    ⇒ Ordinate at D' =
    1
    		× 5 = 0.25
    20

    If udl is loading span PR, we get maximum SF just to the right of Q
    ⇒ SF =
    1
    		× 0.25 × 10 +
    1
    		× 20 × 1× 4
    22

    SF = 45 kN

    Correct Option: C

    When a cut is made just to the right of Q and displacements are given such that A'B' is parallel to B'C'. is very close at Q, displacement of B' to the left will be zero and that to the right will be, 1.

    Hence slope of B'C' = 1/20
    ⇒ Slope of B'A' = 1/20

    ⇒ Ordinate at A' =
    1
    		× 5 = 0.25
    20

    ⇒ Ordinate at D' =
    1
    		× 5 = 0.25
    20

    If udl is loading span PR, we get maximum SF just to the right of Q
    ⇒ SF =
    1
    		× 0.25 × 10 +
    1
    		× 20 × 1× 4
    22

    SF = 45 kN

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

    What is the magnitude of maximum shear stress in MPa?








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    = 60 ± 50
    σ1 = 110
    σ2 = 10

    ∴ τmax =
    σ1 - σ2
    		=
    110 - 10
    		= 50 MPa
    22

    Correct Option: A


    = 60 ± 50
    σ1 = 110
    σ2 = 10

    ∴ τmax =
    σ1 - σ2
    		=
    110 - 10
    		= 50 MPa
    22