Question

A P - force system is given as (50 kN, 25 kN, - 30 kN) and another force system Q is given as (Q kN, 15 kN, - 25 kN). The deflection due to P - force system in the direction of Q is (0 mm, 2 mm, 4mm) and the deflection due to Q - force system in the direction of P is (-2mm, 0 mm, - 1 mm). The value of Q is:

• A. 22.5 kN
• B. 37.5 kN
• C. 47.5 kN
• D. Any value

Answer 1

The correct option is D Any value

Given,
P = (50 kN, 25 kN, - 30 kN)
Q = (Q kN, 15 kN, - 25 kN)
${\Delta }_{PQ}=(-2mm,0mm,-1mm)$
${\Delta }_{QP}=(0mm,2mm,4mm)$
$\sum P{\Delta }_{PQ}=\sum Q.{\Delta }_{QP}$
$50(-2)+(25\times 0)+(-30)\times (-1)=(Q\times 0)+(15\times 2)+(-25)\left(4\right)$
$-70=-70$
So, Q can be any value.