Max Stresses of Unequal Steel Angles

[vcueto80]

I have an unequal steel angle and have been trying to calculate the maximum tensile and compressive bending stresses by hand. Since this is the first time I am doing one by hand I want to make sure my procedure is correct, so I took a problem from a textbook (Advanced Strength and Applied Stress Analysis, 2nd Ed., by Richard G. Budynas). I’ve tried numerous times to solve the problem but I cannot seem to get the answers that are given in the textbook. I have attached the problem with the answers. Can anyone get the answers or approximately? If so maybe tell me what I am doing wrong.

I have read the forum Principle Axis Bending of Single Angles and it has helped somewhat. The problems that I see I might be doing wrong is the signage & location of max stresses . But like I stated earlier I tried numerous times to solve the problem.

One other thing, the textbook gives many other problems and examples (involving unsymmetrical beams) and I have been able to solve the max stresses. But for an unequal angle I think I am doing something wrong. Someone help, please!


This might be helpful IZ = 0.225 in4 & other principle axis let’s call it Iw = 1.257in4
These are the approximate locations I have been using to try to get the max stresses measured from the principle axis.
1. z = -1.0 in, w = 1.5 in
2. z = -2.0 in, w = -0.4 in
3. z = 0.73 in, w = 0.85 in
signs might be wrong ±

 

[desertfox]

Hi vcueto80

It would be helpful if you can tell us what the angle is going to be used for.
Also can you scan your workings out so that we might see better were your going wrong

desertfox

 

[cntw1953]

1. Follow through one of the example problem on the text book. 2. Then do it again with text closed and check results. 3. If correct, do it again with your loadings and properties. If stumble over step 2, repeat 1 & 2 until you have firm grab on the example.

Good luck, that's the way how I learned.

 

[vcueto80]

Eventually I want to get to where I can calculate the max stresses and deflections of steel lintels to support brick without any continuous lateral-torsional restraint without using any programs. Once I have a good feel for unequal angles, I then want to proceed to part 16 section F10 Single Angles from the Steel Construction Manual 13th ed.

cntw1953
I have looked at the example problems and have solved many other unsymmetrical sections but when it comes to this one problem I cannot seem to get the author's numbers.

desertfox
i will scan my workings here shortly

 

[desertfox]

Hi vcueto80

Thanks i will try and help

 

[cntw1953]

Did you break down Mz onto moments acting in direction of the principal axes, from there you can determine min/max stresses locations by observation.

If I remember correctly, you can also work out the cross-product moment of inertia, then use generalized bending formula to solve this problem.

 

[vcueto80]

Here you go, can you see if my procedure is somewhat correct? Thanks

 

[cntw1953]

Mz (on principal axis) should be negative (acting in negative direction of Z-Z).

 

[jrw501]

As someone else suggested, I think you need to use the general bending equation,

stress=[(MxIy-MyIxy)/(IxIy-Ixy^2)]*y+[(MyIx-MxIxy)/(IxIy-Ixy^2)]*x

The equation M*y/I is a special case when Ixy-->0 (for sections with at least one axis of symmetry).

 

[vcueto80]

jrw501

You can also use the equation you just listed, I used the principal axes. The disadvantage I had was the transformation of the coordinate system. I way having trouble with the signage(if it was plus or minus). I did it my way since the Steel Manual provides you with the principal axis angle and moment of inertia. From there all I need is to calculate the max distances from the principal axis. If I used the general bending equation I would have to calculate Ixy. Thanks

cntw1953
thanks for your help

 

[cntw1953]

No need to mention. I struggled in the past as well.

 

[BAretired]

vcueto80,

I haven't the foggiest idea of what to make of your pdf. Would you mind explaining what it means?


BA