Determine the required cross sectional areas

Question

Determine the required cross-sectional areas of members AB and AD of the given truss shown, if the allowable stress in tension is 120MPa while in compression is 105MPa. A reduced allowable stress in compression is given to reduce the danger of buckling.

Link to image: https://imgur.com/SGlzZJc

Answer 1

Step 1 - Inspection

1. By inspection member AD is a zero force member hence there is no stress.

Step 2 - Method of Sections

1. Cut through members AB, AC, & CD
2. ∑Mc = -75(2)-50(4)+AB(3/5)(4)=0, ∴ AB = 145.83 kN (T)

Step 3 - Cross Sectional Area

1. Member AB is in tension, using the equation for stress (σ) = F/A. Given that the allowable stress in tension is 120 MPa, therefore A = F/σ = (145.83 x 10³)/(120x10⁶)=1.22*10^-3 m².