Principal Stress and Maximum Shear Stress

[steevee]

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.

 

[SteamKing]

The next step would be to start calculating bending and shear stresses at the requested locations.

Once you have calculated those stresses, you may use Mohr's circle to calculate the principal stresses.

 

[steevee]

Thanks for your reply SteamKing

Do you mean σx, σy and τxy? If so, how do I do this?

 

[SteamKing]

You've put down the formulas. Don't you know how to use them?

 

[steevee]

I think I understand how to get τ but I'm not so sure about σx and σy
The equation is σ = (M/I)×y right? Is this σx or σy?

Also I'm not sure if the method I used to calculate Ixx was correct. Is it as simple as splitting it into three smaller sections because the examples we have covered in class involved integration.

 

[steevee]

Bump. Can anyone help please?