Determine the horizontal of joint D of the rigid jointed plane frame as shown in fig.,due to change of temp.of member surfaces.Consider depth of all the members as 500mm.Take $\alpha_t=12 \times 10^{-6}/^0$

Mumbai University > Civil Engineering > Sem 5 > Structural Analysis – II

Marks: 10 Marks

Year: May 2015

Apply unit weight of 1 KN at D ,

Apply condition of equation,

$ΣMA = 0 \\ -1 * 3 + MA = 0 \\ MA = 3 KN-m \\ ΣFY =0 \\ VA = 0 \\ ΣFX = 0 \\ -HA + 1 = 0 \\ HA = 1$

h = depth of all members = 500 mm = 0.5 m

Apply Mohr’s Equation ,

Displacement $= αt * Σ [ ( Δt / h ) * A + tc * N * L ] \\ = 12̂ * 10^-6 [ ( 40 * -2.5 + 30 * 0 ) + ( 30 * 12 + 22.5 * 1 * 4 ) + (20 * 2 + 15 * 0 ) ] \\ = 5.16 * 10 ^ -3 m = 5.16 mm$