Which one of the following is correct statement regarding the tru
Which one of the following is correct statement regarding the trusses shown below:
A. I will have less member force and less deflection at B, compared to II
B. I will have less member force and more deflection at B, compared to II
C. I will have more member force and more deflection at B, compared to II
D. I will have more member force and less deflection at B, compared to II
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Force in member AB and BC will be same
2F sinθ = P
\({F_I} = \frac{P}{2}.\frac{1}{{sin\theta }}\) ----for (I)
\({F_{II}} = \frac{P}{2}.\frac{1}{{\sin \left( {\frac{\theta }{2}} \right)}}\) ----for (II)
as sinθ > sin (θ/2)
FI < FII
Now there will be only vertical deflection at joint B, no horizontal deflection
Deflection, \(\delta = \frac{{\delta U}}{{\delta F}}\)
Again, strain energy, \(U = \frac{{{F^2}L}}{{2AE}}\)
So, as member force is less, strain energy will also be less in truss I, Thus the deflection in truss I will also be lesser than truss II.