Mechanical and structural analysis miscellaneous

Mechanical and structural analysis miscellaneous

Easy Questions

Mechanics and Structural Analysis

Mechanical and structural analysis miscellaneous
  1. Consider a bar of diameter ‘D’ embedded in a large concrete block as shown in the following figure, with a pull out force P being applied. Let σb and σst be the bond strength (between the bar and concrete) and the tensile strength of the bar, respectively. If the block is held in position and it is assumed that the material of the block does not fail, which of the following options represents the maximum value of P?








  1. View Hint View Answer Discuss in Forum

    Bond strength = σb × outer area of bar embedded
    = σb × πDL
    Tensile strength = σst × (π/4)D2
    Max. value of P is the minimum of bond strength & tensile strength

    Correct Option: B

    Bond strength = σb × outer area of bar embedded
    = σb × πDL
    Tensile strength = σst × (π/4)D2
    Max. value of P is the minimum of bond strength & tensile strength

  1. 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?








  1. View Hint View Answer Discuss in Forum

    The portion QR has a varying twisting moment with a maximum value of WL.

    Correct Option: B

    The portion QR has a varying twisting moment with a maximum value of WL.

  1. The value of W that results in the collapse of the beam shown in the following figure and having a plastic moment capacity of Mp is








  1. View Hint View Answer Discuss in Forum

    Indeterminacy = 1
    ∴ no. of plastic hinge for mechanism = 2 (at A & C)

    In ∆ABD & CBE

    AD
    		=
    AB
    CECB

    ∴ CE =
    MP.3
    		=
    3MP
    1010

    ∴ MP +
    3MP
    		=
    ω × 7 × 3
    1010

    ⇒ ω =
    13MP
    21

    Correct Option: D

    Indeterminacy = 1
    ∴ no. of plastic hinge for mechanism = 2 (at A & C)

    In ∆ABD & CBE

    AD
    		=
    AB
    CECB

    ∴ CE =
    MP.3
    		=
    3MP
    1010

    ∴ MP +
    3MP
    		=
    ω × 7 × 3
    1010

    ⇒ ω =
    13MP
    21

  1. A three hinged parabolic arch having a span of 20 m and a rise of 5 m carried 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








  1. View Hint View Answer Discuss in Forum

    Take moment about A, ´
    VB × 20 = 10 × 5
    ∴ VB = 2.5 kN
    VB × VB = 10
    ∴ VA = 7.5 kN
    Take moment about C, to right.
    HB × 5 = VB × 10
    ⇒ HB = 5 kN
    Resultant of HA and HB

    = 9.014 kN
    RA cos θ = HA

    ∴ cos θ =
    5
    9.014

    ∴ θ = 56.31°

    Correct Option: A

    Take moment about A, ´
    VB × 20 = 10 × 5
    ∴ VB = 2.5 kN
    VB × VB = 10
    ∴ VA = 7.5 kN
    Take moment about C, to right.
    HB × 5 = VB × 10
    ⇒ HB = 5 kN
    Resultant of HA and HB

    = 9.014 kN
    RA cos θ = HA

    ∴ cos θ =
    5
    9.014

    ∴ θ = 56.31°

  1. A disc of radius r has a hole of radius r/2 cut-out as shown. The centro id of the remaining disc (shaded portion) at a radial distance from the centre ‘O’ is








  1. View Hint View Answer Discuss in Forum

    New area = πr2 - π(r/2)2

    =
    3πr2
    4

    Distance from centre to new centro id
    x =
    πr2 × 0 - π(r/2)2 × r/2
    3πr2
    4

    =
    - r
    6

    ∴ x =
    r
    		(away from centre)
    6

    Correct Option: C

    New area = πr2 - π(r/2)2

    =
    3πr2
    4

    Distance from centre to new centro id
    x =
    πr2 × 0 - π(r/2)2 × r/2
    3πr2
    4

    =
    - r
    6

    ∴ x =
    r
    		(away from centre)
    6