Question

Two steel truss members, AC and BC, each having cross sectional area of $100m{m}^2,$ are subjected to a horizontal force F as shown in figure. All the joints are hinged.

The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is

• A. 8.17
• B. 11.15
• C. 14.14
• D. 22.30

Answer 1

The correct option is B 11.15

Method I :
Maximum force = 0.8965 F

$\therefore \text{Max stress}=\frac{0.8965F}{100}\le 100MPa$

$\therefore 100\ge \frac{0.8965\times F}{100}$

$\therefore F\le 11.154kN$

Method II:
$As,F_{AC}=0.895kN$
then

$\frac{F\times F_{AC}}{A}=100$

$\frac{F\times 0.895}{100}=100$

$F=11173.18N=11.173kN$