Calculate Maximum Load of a Beam

[1question]

Homework Statement

The bar 1 in the figure has a cross-sectional area of 0.75 in^2. If the stress in this bar must be
limited to 30 ksi (30,000 psi) determine the maximum load that P that can be supported by
the structure.

Homework Equations

σ = F/A
τ = Fd

The Attempt at a Solution

σ = F/A
F = (30,000 psi)(0.75 in^2)

τ = Fd
τ = [(30,000psi)(0.75in^2)](6ft) --- torque/moment about B.

Then equate to second torque as change distance and force, but still same torque. To clarify, I mean τ = F₁d₁= F₂d₂
aka τ = (force in beam 1)(6ft) = (P)(10ft)

τ₂ = F₂d₂=(30,000psi)(0.75in^2)(6ft)
F₂(10ft) = (30,000psi)(0.75in^2)(6ft)
F₂= (30,000psi*0.75in^2*6ft)/10ft
F₂= 13500 lb ft

That should be reasonable as the original force (@ beam 1) would have been 30000*0.75 = 22500 lb ft. Since the distance to P is larger, the force should be smaller (and it is) to keep the torque the same.

Is there anything wrong with this answer or my method? We are studying considerably more difficult material, so I question the above easy solution.

 

[Maiq]

Yep your work looks right to me. This is a pretty basic problem so if you know what your doing it will seem easy.
Don't worry though you'll get more difficult questions eventually.