# simply supported at both ends round beam

• Dec 9th 2009, 06:55 AM
JAW
simply supported at both ends round beam
I've been working on this problem for 3 days now and i now pulling my hair out.. Can someone please help..

The question comes in to parts, and i'm resonably happy with part 1.

Part 1. A round beam is simply supported at both ends and carries a unformly distributed load over its entire top surface. Determine the maximum load (N/m) such that the radius of curvature does not exceed 23m. Assume that the diameter is 200mm the length is 4m and the modulus of elasticity of wood is 10GN/m^2.

Answer:- By use of the formula E/R = M/I = O/y

Ixx of a circle = pye x D^4/64
=pye x 200^4/64
=78539816.34mm^4

M =EI/R
= 10x10^9 x 7.854x10^-5/23
= 34.148 kN/m

BM = Wl^2/8

W=Mx8/L^2
= 34.148x10^3 x8/4^2
=17.074 kN/m

i believe this to be correct up to this point. Please advise.

Part 2. It is decided to strengthen the beam by adding two 20mm diameter steel rods, one to the top surface and one to the bottm surfsce, each to run the full length of the beam. Dtermine the new load capacity for the same radius of curvature. Assume that the modulas of elasticity for steel is 210GN/m^2.

SMOA of 1 x steel rod as follows.

Ixx= pye d^4/64
=pye x 20^4/64
7853.982mm^4

using parallel axis therom Ioo = Ixx+ah^2

7853.982 + 2(pye x 10^2 x 110^2)
= 7610508.204mm^4