## Beam under Biaxial transverse load - Von Mises Stress calculation

## Beam under Biaxial transverse load - Von Mises Stress calculation

(OP)

Hi everyone,

It might seem like too simple a Question for many but I would like to calculate the Von Mises stress for a beam in biaxial bending. The bending stresses run along the beam axis so they can be added up at the Cross section Corners, but I would like to find the maximum Von mises stress including the components of shear stress as well. There is also an axial load on the beam, that generates its own normal stress. I have attached a diagram for explanantion.

At which Point on the Body should the Von mises stress be calculated to obtain a maximum value?

My bending stresses are 303 MPa for Sigma bxk, and 408 MPa for Sigma bxs(Qz,) and maximum txz (Qz) is 16 MPa, and maximum txy is 132 MPa.

Thank you all in advance

Regards

Asutosh

It might seem like too simple a Question for many but I would like to calculate the Von Mises stress for a beam in biaxial bending. The bending stresses run along the beam axis so they can be added up at the Cross section Corners, but I would like to find the maximum Von mises stress including the components of shear stress as well. There is also an axial load on the beam, that generates its own normal stress. I have attached a diagram for explanantion.

At which Point on the Body should the Von mises stress be calculated to obtain a maximum value?

My bending stresses are 303 MPa for Sigma bxk, and 408 MPa for Sigma bxs(Qz,) and maximum txz (Qz) is 16 MPa, and maximum txy is 132 MPa.

Thank you all in advance

Regards

Asutosh

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

doubly symmetric beam ? (so the orthogonal axes are also the principal axes)

what's the stress state in the corners of the beam ? sum of the bending and axial normal stresses with no shear ?

another day in paradise, or is paradise one day closer ?

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

If this were practical steel design, then von mises is not relevant as some degree of plasticity is acceptable and encouraged by codes when undertaking design checks.

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

Just wanted to know what the engineering community does for such cases.

Thanks :)

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

if metal, why are you bothering with von Mises ? sum the normal stresses from bending and axial, if you really want, look at principal stress at a section with less than maximum bending stress (probably not critical, or significantly different to the peak bending stress. for max shear, on CL/centroid, make a principal stress from axial normal and bending shear stress. Von Mises combines different (orthogonal) principal stresses together, something you get in a prismatic section … you have a prismatic metal beam ??

another day in paradise, or is paradise one day closer ?

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

Agreed that von Mises is usually not useful in beam design in a practical sense. von Mises to me is most useful because it combines shear and axial stress and gives you a stress which is comparable to the axial yield strength. We normally only use principal stresses for brittle materials like glass.

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

I would say the problem proposed is a bit funny; more theoretical than practical.

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation

for me, vm for this example collapses to max principal which collapses to max normal stress (bending + axial). why make things more complicated than they need to be ?

this would probably not be true for a concrete beam.

another day in paradise, or is paradise one day closer ?

## RE: Beam under Biaxial transverse load - Von Mises Stress calculation