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supported beam

Submitted by Dimitris S. An… on

Hello.

I am a physics teacher who work also as a researcher in applied mechanics (gradient elasticity and couple stress elasticity).

Nevertheless, I must admit that I have some serious gaps in basic

mechanics of materials theory.

Recently a student of mine, came up with the following query:

"Let a rod of weight w and length L is supported by two tables. Half of the rod is suported by one of the table and L/4 of the rod is supported by the other table. Find the forces that the rod is acted upon by the tables."

I think that this problem does not have a single solution within rigid body mechanics.

I am familiar with various types of supports but I never came across a distributed

support.

 I tried to model the situation with α formation of distributed srings (I saw it from a naval engineering text) but I do not know how to go on.

If the solution is too exhaustive it suffices to treat the rod as rigid body.

I would appreciate any kind of assistance.

Thank you very much (...and Happy new year!)

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yawlou

Please could you clarify your question.

1.  When you say "tables" do you really mean cables?

2.  When you say half of the bar is supported by one cable and L/4 is supported by another cable, it appears you have a discrepancy since L/4 of the bar is then not supported by anything.

 A picture would be very helpful.  Then perhaps some assistance might be provided.

regards,

Louie

Sun, 01/01/2012 - 21:30 Permalink
George Mokios

According to the cofiguration you are describing, you get two distributed reaction forces:

w1, spanning from 0 to L/2 (suppose you measure length starting from the far left end of the beam)

w2, spanning from 3L/4 to L.

Equivalently, you have two reaction (point) forces:

f1, at L/4

f2, at 7L/8

You need to equilibrate forces (f1+f2 = w) and moments. For the moments, pick L/4 as the reference point. You end up with f2*5L/8-w*L/4 = 0. These are two equations for the two unknowns, f1 and f2.

Solve, and you get f1=3*w/5 and f2=2*w/5.

This is plain old statics. All of the above are valid under the following assumptions:

1. The two tables and the bottom surface of the rod are flat and they all lie on the same level.

2. The rod is homogeneous throughout its length (no weight/cross section area variations along its length)

3. Reaction distributed loads w1 and w2 are constant along L (consequence of assumptions 1 & 2)

4. Everything is rigid

Mon, 01/02/2012 - 08:46 Permalink