The rigid beam is supported by the three suspender bars Bars

The rigid beam is supported by the three suspender bars. Bars AB and EF are made of aluminum and bar CD made of steel. If each bar has a cross-sectional area of 450 mm^2 determine the maximum value of P if the allowable stress is (alpha_allow)_st = 200 MPa for the steel and (alpha_allow)_al 150 MPa for the aluminum. E_st 200 GPa, E_al = 70 GPa.

Solution

We will first calculate force in each bar

Given,crossectional area of each bar= 450 mm²

Allowable stress in bar of steel=200 MPA and allowable stree in aluminium bars=150 MPA

Now calculating force in each bar.let the force in each bar be P

Calculating force P in bar AB which is an aluminium bar

= stress in bar AB x crossectional area of barAB= 150 MPAx 450 mm²=150x10⁶ PA x450mm²

=150 N/mm²x450 mm²=67500 N

Force in Bar CD which is a steel bar

=stress in bar CD x crossectional area of bar CD= 200 MPA x 450 mm²=200x10⁶PAx 450 mm²

=200 N/mm²x 450 mm²=90000 N

Force in bar EF

stress in bar EF x crossectional area of bar EF= 150 MPAx 450 mm²=150x10⁶ PA x450mm²

=150 N/mm²x450 mm²=67500 N

Now as per the Force balance equation, the summation of forces F+F2+F3=67500+90000+67500=225000 N------(1)

As given in the diagram above, the summation of Forces is also given by=P+2P----------(2)

Equating the equation (1) and (2) above,

P+2P=225000

3P=225000

P=75000 Newtons.Thus value of force P=75000 N