Statics: help regarding beams.

Jul 2018
3
0
Hi!

I have been working on the following problem:

1. Consider the beam on the figure. Show with the help of a free body diagram how one can calculate forces and momentum on the vertical interface through the beam in a distance 1 m to the right of point C.

2. Show how one can calculate size and distribution of the normal stresses at the interfaces. The beam is a I-profile with moment of inertia I= 22,2*106 mm4 and height = 162 mm.


I use the following equations of equlibrium to part 1:

∑Fx = 0 ∑Fy = 0 ∑Fz = 0

∑Mx = 0 ∑My = 0 ∑Mz = 0.


I apply the equations of equilibrium to the full beam to determine the unknown forces acting on it.

+ ∑Ma = 0: -20 kN(2 m) + Cy(5.5 m) = 0 → 5.5Cy = 40 + 112.5 → Cy = 27,7 kN


↑ + ∑Fy = 0: -Ay – 20 kN + 27,7 kN = 0 → Ay = -20 + 27,7 → Ay = 7.7 kN


→ + ∑Fx = 0: Ax = 0 kN


These might be unnesseary however, since the problem asks how one can calculate forces and momentum on the vertical interface through the beam in a distance 1 m to the right of point C.

So I have made the following:

+ ∑Ma = 0: -20 kN(2 m) + Cy(4 m) = 0 → 4Cy = 40 → Cy = 10 kN


↑ + ∑Fy = 0: -Ay – 20 kN + 10 kN = 0 → Ay = -20 + 10 → Ay = -10 kN


→ + ∑Fx = 0: Ax = 0 kN

But are they correct. Are they the complete answer.


Part 2 confuses me. We are given

I= 22,2*106 mm4
and
h = 162 mm,

so it is probably the elastic flexure formula:
σx = - (Mr y / I)

that should be used. But how do I apply the data. Help is appriciated.
 

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