Stress Combination

[kxa]

Here is something I have been arguing with another engineer about and wanted to what others say. It is a simple question: If you have a horizontal force and vertical force acting at the same time on a beam how the stresses should be added? I am saying that the stresses should be simply superimposed (regardless of the shape) but his thoughts were that the resultant force (sq. root of sum of sq’s) should be used to calculate the max. stress. Any thoughts?

Thanks in advance.

 

[JStephen]

It depends on what you're doing. If you actually want to find the stress at a point, then you'd combine the stresses from the two different loads, use Mohr's circle, etc. However, the structural steel codes are set up so you evaluate tension/ compression, evaluate bending, and then evaluate the combination of these, without actually calculating the combined stress at a point.

 

[corus]

I'd agree with JStephen. Read the design codes and how to assess the stresses, both as principal stresses, individual stress components, and as a combined stress intensity value (which isn't simply the root sum squares). In general you're looking to satisfy the codes against fatigue (if applicable), buckling, and yielding, which are all treated differently and have different stress criterias.

corus

 

[Lion06]

I actually think you'll get the same answer either way. The first thing you would do with a load at some angle is break it into its components (a vertical force and a horizontal force). I see no need to take two forces, make them into one and then break it back into its components.
I would do P/A +or- M/S, making sure to account for any eccentricity of the horizontal (axial)load (if it exists.

 

[Lion06]

Let me clarify, I would construct a shear and moment diagram, but as I said above....... I think you will get the same answer either way.

 

[ARLORD]

Theoretically you should get the same results. However, in practice I thing it would be harder to use the resultant to get results. Most equations and analysis procedures are set up to work with components of the resultant, not the resulant that doesn't act along the orthogonal axis.

 

[shin25]

It probably depends,

For connection, you have to consider the combined effect of both.

For Beams, these forces will create shear and bending, so should handle as per code.

For columns, as structuralEIT has mentioned.

For other members, use your judgement.

 

[Lion06]

The OP did say this was a BEAM. I don't think there is a code requirement for ANALYSIS. You would have to satisfy code requirements for design of the beam to resist the loads, but the actual stresses would be computed with no code input/requirements (I should make it clear I am assuming this is a steel beam since you likely wouldn't be checking stresses for a concrete beam).
Given the axial load, you could also take the secondary moment of the internal axial force times the deflection at that point, but this may not be necessary for what you are doing and also would affect both of your approaches the same way.
I still say you will get the same answer with both approaches.

 

[rb1957]

the caveat I'd apply to superposition is there could be interaction between the loadings that superposition would miss ... consider beam columns.

the advantage that a vector load would have would be bending of an odd shaped section, where the load has to be resolved onto the principal axes for bending; with components you'd have to do this twice.

 

[Lion06]

rb1957-
can you please elaborate? I am not seeing your point. If I were given a beam-column to analyze and it had a single load on it at some angle (theta), the very first this I would do is resolve this load into the vertical and horizontal components (or a load along the axis of the member and perpendicular to the axis of the member), then construct a shear and moment diagram.
I am not following you. How would you approach this seemingly VERY simple analysis?

 

[prost]

As long as the deflections and strains are 'small', then superposition (calculating the stress due to each force separately and adding) will work. Not being familiar with these codes, how does the 'answer' obtained this way differ from the answer in the code?

 

[csd72]

It will work out the same stress for beams that have the 4 corners in a square.

Where it wont work is circular sections(or pipes) these would have the maximum stresse at different points. You should always get the resulant moment for circular members.

The one drawback with getting the resultant is that you dont get the benefit of the larger allowable stress around the minor axis. Also how do you calculate for buckling?

All the code clauses are based on major and minor axis treated separate.

csd

 

[rb1957]

beam column ... you can't superimpose the axial load and the transverse load (just an observation about superposition, sounds like you know enough not to do it in the 1st place).

 

[shin25]

StructuralEIT,

The reason I have mentioned code is because, for beams, per code the shear and bending can be handled seperately. Even though the resultant combination of these two will be more than the indivisual stress.

 

[rb1957]

kxa,
could your collegue mean that it is more conservative to apply the vector, and so "better" ?

 

[zaes73]

after reading all the views i have actually analysed a 10ft beam and Applied to it a load combination case of Lateral point(GFz) load + then a point load on top (GFy). then i calculated the resultant force with pythogras thoerm and applied that force to the beam.

the resulting stresses Bending and torsional are almost the SAME !

 

[UcfSE]

zeas73, did you try that with an "I" shaped beam?

 

[darkwing88]

Read the applicable code.

There is no combining of shear and normal stresses for a steel beam using the AISC code.

Re: Sections F4 and H1 of AISC 9th Ed.

 

[miecz]

I believe the OP was asking about the bending stresses in an I-beam with load in the direction of the major and minor axes. No axial force. The 9th Ed. AISC code handles this with Eq. 1.6-2, which gives the benefit of the larger allowable stress around the minor axis.

The combined stress for an I shape, incidentally, is not the sq. root of sum of sq’s., but the sum of the stresses, i.e., f_total=f_a+f_b.

I agree that a round shapes and those with axial force are handled differently, but I don't think that's what the OP had in mind.

 

[darkwing88]

Whatever. Same reference.