In the truss shown in the figure no load acts. The members AB gets 4 mm too short. The cross-section area of each member is 300 $m m^{2}$ and E = 200 GPa. Determinate the vertical displacement of 30 m at joint C.

1.2 mm upward

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1.5 mm upward

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1.2 mm downward

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1.5 mm downward

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Solution

The correct option is B 1.5 mm upward
$S i n θ = \frac{4}{5}$

$C o s θ = \frac{3}{5}$

The vertical displacement at joint 'C'

$δ_{v o} = \sum K Δ$

$= K_{A B} (- Δ_{A B})$

$= \frac{3}{8} (- 4) = - 1.5 m m$

The negative sign indicate that joint 'C' is displaced upward i.e opposite to the unit load.

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In the truss shown in the figure no load acts. The members AB gets 4 mm too short. The cross-section area of each member is 300 mm2 and E = 200 GPa. Determinate the vertical displacement of 30 m at joint C.

The correct option is B 1.5 mm upwardSinθ=45 Cosθ=35 The vertical displacement at joint 'C' δvo=∑K Δ =KAB(−ΔAB) =38(−4)=−1.5 mm The negative sign indicate that joint 'C' is displaced upward i.e opposite to the unit load.

In the truss shown in the figure no load acts. The members AB gets 4 mm too short. The cross-section area of each member is 300 $m m^{2}$ and E = 200 GPa. Determinate the vertical displacement of 30 m at joint C.