# Homework Help: Uniform beam reinforced with iron, how to approach?

1. Mar 19, 2015

### Alex Santos

So I am starting to learn for the final exam a bit early and I am trying to do this problem with a uniform beam which is reinforced with iron inside. I know how to calculate this if it wasn't for the reinforcement within the concrete. I know that the purpose of the iron reinforcement is to account for shear stress but I do now know how it involves in my equations or which equation I use.
Can someone explain how to approach these kind of problems in general?
Picture of the problem is in the link

1. The problem statement, all variables and given/known data

So I am suppose to find the maximum force q so that the normal stress within the beam caused by momentum is within allowed constraints.
qw is the weight of the beam and q is the external force applied

physical properties of concrete: EC = 20GPa, tension σ t Y C = 3MPa and compression σ c Y C = 30 MPa. physical properties of iron Ei = 190GPa, tension σY i = 400MPa. density of the beam is γ = 24kN/m3 . moment of the inertia I = bh3/12

2. Relevant equations

3. The attempt at a solution
I have done anything so far because I do not know where to start.

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2. Mar 21, 2015

### Staff: Mentor

Why don't you start out with what you can do, which is writing out your shear and moment equations? What is your solution to the problem if the steel reinforcement wasn't there (if you can't get that, then you certainly won't be able to do it with the reinforcement present)? Can you guess how the tensile strain would vary with position through the thickness of the beam with and without the steel reinforcement present?

Chet

3. Mar 30, 2015

### pongo38

Although the iron does make a contribution to shear resistance, its orientation longitudinally means that its main purpose is to strengthen the bending resistance. You need to to study 'elastic analysis of composite sections' in order to develop the equations you require. This requires you to develop an equivalent section made of one material, but with different geometry, so that you can apply the knowledge you now have.