Shear Stress equation in Beams

Nexus305

I was working on a question where I had to find the maximum shear stress in a I-beam due to a shear force applied on it. Heres the question :

An I girder 600 mm x 300 mm has flanges 25 mm thick and a web 13 mm thick. Find the maximum shear stress due to a shear force of 500 kN and compare this value with the common approximation.

For this my lecturer used this equation : τ = F/Ib ∫ _y1^600/2 y dA and he took y1=0

Can someone please explain how to use this equation because I dont understand the integration part from ybarA to 600/2. I dont understand how he got the limits of the integration.

Thanks!

Studiot

Well your lecturer is using the horizontal shear stress formula


[tex]{S_s} = \frac{V}{{Ib}}\int\limits_{{y_1}}^c {ydA} [/tex]

for horizontal shear at a distance y from the neutral axis, under vertical shear V

The first limit is taken a zero because the shear in the web is neglected as insignificant so y1 corresponds to the underside of the flange.

The second limit c is the distance from the neutral axis to the free surface of the beam, thus c=600/2

Nexus305

I have another doubt. In such a situation, where exactly in the I-beam does the maximum shear stress occur?

anicolajsen

The shear stress in a beam subjected to a point load is constant accross the entire length of the beam assuming the load is applied at midspan.

Unless your talking about shear flow caused by bending of the beam. In this case the maximum shear occurs at the location of the applied point load as this is the point of maximum bending moment.

Studiot

Welcome anicolajsen
I think you will find the subject here is about the stress distribution across the section, not the beam length. No infomation as to the nature and location of the loads and supports was provided. Would you regard the I section specified as in need of wide flange corrections?