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steevee

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## Homework Statement

Hi all,

For my CW I have a question on a simple beam, ABCD and its cross-section. Please see attachment for figures

The material of the beam is steel, where modulus of elasticity, E = 210 GN/m^2

I have been asked to calculate the principle stresses and the maximum shear stress at the top of the beam for the loaded system and 2 m from the left of the beam.

## Homework Equations

x-bar = (A1x1 + A2x2 + A3x3)/(A1 + A2 + A3)

y-bar = (A1y1 + A2y2 + A3y3)/(A1 + A2 + A3)

Ixx = bd^3/12 + Ah^2

τ = (VAy-bar)/bI

M/I = σ/y = E/R

## The Attempt at a Solution

I have worked out the roller support (A) = 94166.67 N and hinge support (D) = 90833.33 N

Next I drew a shear force diagram and a bending moment diagram. From the diagrams, max shear force = 94.17 kN and max bending = 243.33 kNm

Following on from this I concentrated on the z-bar cross-section. I divided the section into three sub-sections and calculated the area of each part and their centroids. From this I calculated x-bar and y-bar and started to calculate Ixx using Ixx = bd^3/12 + Ah^2

I want to ask whether I am on the right lines because I don't know how to carry on from here.

#### Attachments

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