17-42. The ideal column is subjected to the force F at its midpoint and the axial load P. Determine the maximum moment in the column at midspan. El is constant. Hint: Establish the differential equation for deflection, Eq. 17-1. The general solution is v = C1 sin kx + C2 cos kx – cx/k?, where c² = F/2EI, k² = P/EI.

*17-48. The aluminum column is fixed at the bottom and free at the top. Determine the maximum force P that can be applied at A without causing it to buckle or yield. Use a factor of safety of 3 with respect to buckling and yielding. E = 70 GPa, oy = 95 MPa. %3D -5 mm 150 mm 10 mm-- 80 mm =10 mm 80 mm 5 m

17-15. Determine the maximum load P the frame can support without buckling member AB. Assume that AB is made of steel and is pinned at its ends for y-y axis buckling and fixed at its ends for x-x axis buckling. Est = 200 GPa, oy = 360 MPa. -3 m- HA 50 mm х 4 m 50 mm - 50 mm

Determine the load P if the end C is displaced 0.075 in. downward.