Calculate Out of Plane Deflection Curve

2018-03-21 17:24:28

First of all, this is not a homework question.

I simply have a hard time finding relevant sources or help. Therefore, I am asking this question here. Hopefully, someone can help me.

I would like to calculate the analytic solution of the deflection curve of the L-Shaped cantilever beam as shown in the following image:

It is difficult, because the force acts out of the plane, and will therefore induce an out of plane bending of the cantilever. The cantilever will exhibit torsinal and bending stress.

For the L2 part the deflection is $$PL^3/3EI $$ considering it a simple cantilever beam with L= L2-W1

The L1 with the L = L1+ W2 has two deflections. first acting as a cantilever under load P. Second twisting under the torque P(L2-W1).

This is simplifying the stresses in the small corner rectangular W1.W2.

From Roark Formulas hanbook,

twist per inch length = T/(KG)

$$K = ab^3*[16/3-3.36*(b/a)*(1-((b/a)^4)/12)]$$

a = long side, W ; b = short side, T.

T =Torque in

  • For the L2 part the deflection is $$PL^3/3EI $$ considering it a simple cantilever beam with L= L2-W1

    The L1 with the L = L1+ W2 has two deflections. first acting as a cantilever under load P. Second twisting under the torque P(L2-W1).

    This is simplifying the stresses in the small corner rectangular W1.W2.

    From Roark Formulas hanbook,

    twist per inch length = T/(KG)

    $$K = ab^3*[16/3-3.36*(b/a)*(1-((b/a)^4)/12)]$$

    a = long side, W ; b = short side, T.

    T =Torque in-lb

    L= Length in inches

    G = Modulus of rigidity

    This is twist per inch length, you multiply by L.

    You now add the deflection of the L1 under cantilever action to the axis of L1.

    You can modify theese results by considerin the small rectangula W1.W2 strains too.

    This is kind of a rough first estimate. Just to give you preliminary numbers.

    2018-03-21 18:06:41