Steel beam question When a steel b 4

[tony1851]

Steel beam question
When a steel beam deflects under load, the bottom flange is in tension abd the top flange in compression. How would I calculate the (admitedly small) increase in length of the bottom flange, and coresponding decrease in length of the top flange?

 

[msquared48]

Calculus, Trig, and Geometry.

The deflection is at the centerline of the beam where the length does not change. Integrate the deflection equation two more times to get the rotation angle, and use trig to add/delete the increase/decrease to the centerline distance.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[GregLocock]

In simple beam theory the assumption is that plane sections remain plane in bending. So for moment M, etc M/I=sigma/y where y is the distance of the fibre from the neutral axis and R is the radius of curvature. E=stress/strain of course.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[BAretired]

The unit strain 'e' in a bar under stress 'σ' may be determined by the expression e = σ/E where E is the modulus of elasticity of the material. If the stress is constant from end to end, the total strain is e*L where L is the length of the bar.

If the strain is not constant from end to end, the strain is e_av*L where e_av is the average strain in the bar. The change in length of a flange of a beam under load is e_av*L.

e_av depends on the moment variation. If a beam has equal and opposite end momenta 'M'. the unit strain is constant throughout the length. Then e = My/I where y is the distance from the centroid to the center of the flange. Change in length would be e*L.

If the beam has a concentrated load at midspan, the moment varies from 0 at each support to PL/4 at midspan. Unit strain in each flange varies from 0 at each support to PL*y/4EI. Total strain is PL*y*L/8EI.

For other load distributions, the total change in length of a flange may be found by integrating e*dx over the full span.

BA

 

[tony1851]

Thanks guys for your pointers; most informative and helpful

 

[KootK]

Your calculated deflection will give you a curve representing the beam at the height of the neutral axis. Offset this curve downwards by the distance from the neutral axis to your extreme tension fibre and the length of that offset curve should be your answer. Of course, this is only technically correct if you're in "small deflection" territory. If that assumption doesn't apply, you would have to account for the ends of your beam moving closer together.