I really hate my statics book (hibbeler 12th edition). There are no example solutions of any three force members, and the author only spends one sentence describing parallel three force members! I was able to figure out the numerical method with trial and error, but I would appreciate it if someone could explain it to me in words.
The answer in the back of the book says the angle is 1.02 degrees. So I took the tangent of that angle and tried combinations of the numbers given in order to find something that worked. I assumed that the spring at A is compressed meters since the applied force is only a meter away. dividing .16 by 3 (length of the beam) and doing tan inverse gives me
. Dividing by 3 again gives me the answer in the back of the book, or what they most certainly had approximated, 1.0176275 degrees.
If this is incorrect, I would really appreciate some guidance. And even if my method is correct, the physics going on is not obvious to me. Wouldn't the applied force create a larger torque in the opposite direction about B? Does the larger moment at B essentially assist in raising up the opposite end of the beam (so that the deflection is only 0.053333 meters, that would elimiate the second division by 3 after the arctan operation)?
I've searched google, wikipedia, and google books, and I can't find any simple "general case" equations that govern three force members of parallel forces.