Worst case scenario would be a = 0. Any deflection of of the end would tend to lessen the bending stress (because the T cos(theta) term opposes the T sin(theta) term).
Yes. The buckling equation for long slender members is Pcr = (pi/L)^2 E I, where Pcr is the critical buckling force, L is the length of the column, E is the modulus of elasticity of the material you're using, and I is the minimum area moment of inertia (second moment of area) for the...
Actually, both the x and y forces contribute to bending stress. Only the x force contributes to axial stress.
From the attached image, the net bending moment is M = T [b sin(theta) – a cos(theta)]. The axial force is just F = T cos(theta). The max normal stress on the cross section would...
Can you attach a sketch or photo? If you're doing large deflections, you get non-linearities from the change in geometry which make the deflection calculations difficult to do analytically. If your deflections are not that great compared to the length of your beam, then you can do it by hand. In...
I'm teaching a class using Shigley's Mechanical Engineering Design. There is a section on deflection of curved members. If you have this text, you'll notice it calculates the strain energy in bending, axial, and shear, as usual. Then it says that there's another "negative" strain energy...