Mechanical and structural analysis miscellaneous

Mechanical and structural analysis miscellaneous

Easy Questions

Mechanics and Structural Analysis

Mechanical and structural analysis miscellaneous

Direction: A rigid beam is hinged at one end and supported on linear elastic springs (both having a stiffness of ‘k’) at points ‘1’ and ‘2’ and an inclined load acts at ‘2’, as shown.

  1. Which of the following options represents the deflections δ1 and δ2 at points ‘1’ and ‘2’?








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    Taking moment about hinge.
    MH = 0
    kδ1 + kδ2.2L = p × 2L
    ∴ kδ1 + 2kδ2 = 2P

    From the figure,
    ⇒ δ2 = 2 × δ1
    (since the distance is l for both)

    ∴ δ1 =
    2p
    		, δ2
    4p
    5k5k

    Correct Option: B

    Taking moment about hinge.
    MH = 0
    kδ1 + kδ2.2L = p × 2L
    ∴ kδ1 + 2kδ2 = 2P

    From the figure,
    ⇒ δ2 = 2 × δ1
    (since the distance is l for both)

    ∴ δ1 =
    2p
    		, δ2
    4p
    5k5k

Direction: In the cantilever beam PQR shown in figure below, the segment PQ has flexural rigidity EI and segment QR has infinite flexural rigidity.

  1. The deflection of the beam at ‘R’ is








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    Deflection at

    R =
    5WL3
    		+
    3W.L2.L
    6EI2EI

    =
    7WL3
    3II

    Correct Option: C

    Deflection at

    R =
    5WL3
    		+
    3W.L2.L
    6EI2EI

    =
    7WL3
    3II

  1. The deflection and slope of the beam at ‘Q’ are respectively








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    Deflection at

    Q =
    WL3
    		+
    (WL) × L2
    3EI2EI

    =
    5WL3
    7EI

    Slope at
    Q =
    WL2
    		+
    WL.L
    2EIEI

    =
    3WL2
    2EI

    Correct Option: A

    Deflection at

    Q =
    WL3
    		+
    (WL) × L2
    3EI2EI

    =
    5WL3
    7EI

    Slope at
    Q =
    WL2
    		+
    WL.L
    2EIEI

    =
    3WL2
    2EI

Direction: Beam GHI is supported by three pontoons as shown in the figure below. The horizontal cross-sectional area of each pontoon is 8 m2, the flexural rigidity of the beam is 10000 kN–m2 and the unit weight of water is 10 kN/m3.

  1. When the middle pontoon is brought back to its position as shown in the figure above, the reaction at H will be








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    δ =
    (P - R)L3
    48EI

    x × A × rw = R'
    (buoyant force, R' = RG = R1)
    ⇒ x × A × w = R'
    ∴ x =
    R'
    80

    2R' + R = 48
    (x + δ).A × δω = R
    ∴ (x + δ) × 8 × 10 = R
    ⇒
    48 - R
    		+ δ =
    R
    2 × 8080

    δ =
    3R - 48
    160

    =
    (48 - R) × 103
    		= 19.2kN
    48 × 104

    Correct Option: C

    δ =
    (P - R)L3
    48EI

    x × A × rw = R'
    (buoyant force, R' = RG = R1)
    ⇒ x × A × w = R'
    ∴ x =
    R'
    80

    2R' + R = 48
    (x + δ).A × δω = R
    ∴ (x + δ) × 8 × 10 = R
    ⇒
    48 - R
    		+ δ =
    R
    2 × 8080

    δ =
    3R - 48
    160

    =
    (48 - R) × 103
    		= 19.2kN
    48 × 104

  1. When the middle pontoon is removed, the deflection at H will be








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    Consider that middle position is removed.
    Reaction, cluts RG = RI = 24 km (48/2)
    This is supported by flotation.
    ∴ A.rω.rω × h = 24
    8 × 10 × h = 24
    h = 0.3 m
    Deflection at H

    =
    PL3
    48EI

    (similar to a simply supported beam)
    =
    48 × 103
    		= 0.1 m
    48 × 10000

    ∴ Total deflection = 0.1 + 0.3 = 0.4 m

    Correct Option: B

    Consider that middle position is removed.
    Reaction, cluts RG = RI = 24 km (48/2)
    This is supported by flotation.
    ∴ A.rω.rω × h = 24
    8 × 10 × h = 24
    h = 0.3 m
    Deflection at H

    =
    PL3
    48EI

    (similar to a simply supported beam)
    =
    48 × 103
    		= 0.1 m
    48 × 10000

    ∴ Total deflection = 0.1 + 0.3 = 0.4 m