Calculate Transverse Loading for Beam: Principle Stress & Strain

[Dell]

for the beam in the diagram

E=2.1e6kg/cm²
Ixx=3600cm⁴

find:
the principle stresses in the beam

the strains ex, ez e(45) found on the strain rosette placed at point 4



i have only managed to find the principle stress z which i found at point 1 --- 1406kg/cm² where would i find the other stresss? how can i find the stress on the x axis? to find z i used -Y*M/I knowing that the maximum moment is at the wall and is -5.0625[t*m]

to find the strains i just divide by E and i get the z strain=6.67e-4 how can i find the x strain? once i find the x strain can i say the shear strain is 0?

 

[Valkarie]

The principal stresses at point 1 are: σx = 0 kg/cm2 σz = 1406 kg/cm2 The strains at point 4 can be found using the following equations: ex = E * (Δx/L) ez = E * (Δz/L) e(45) = E * (Δx/L) * (Δz/L) where Δx and Δz are the changes in length along the x and z axes, respectively, and L is the length of the beam. The shear strain is equal to zero at point 4 because the beam is assumed to be in a pure bending state.

 

[Mene]

I would first like to clarify that the provided information is not sufficient to accurately calculate the transverse loading for the beam. The transverse loading is dependent on multiple factors, such as the type of loading (point load, distributed load, etc.), the beam's supports, and the dimensions and material properties of the beam. Without this information, it is not possible to accurately calculate the transverse loading.

However, assuming that the beam is simply supported and subjected to a distributed load, I can provide some general guidelines for calculating the principle stresses and strains in the beam.

To find the principle stresses, you will need to use the general equation for bending stress in a beam, which is σ = -My/I, where M is the maximum bending moment, y is the distance from the neutral axis, and I is the moment of inertia of the cross section. In this equation, the negative sign indicates that the stress is compressive.

To find the maximum bending moment, you will need to know the type and magnitude of the distributed load and the beam's length. Once you have the maximum bending moment, you can use the equation to calculate the principle stresses at any point along the beam.

To find the strains, you will need to use the equation ε = σ/E, where σ is the stress and E is the modulus of elasticity of the material. As you have correctly calculated, the strain in the z-direction can be found by dividing the principle stress in the z-direction by the modulus of elasticity.

To find the strain in the x-direction, you will need to use the equation ε = -νσ/E, where ν is the Poisson's ratio of the material. This equation takes into account the fact that the material will also experience deformation in the x-direction due to the applied stress in the z-direction.

To determine if the shear strain is zero, you will need to use the equation γ = τ/G, where τ is the shear stress and G is the shear modulus of the material. Without knowing the shear stress, it is not possible to determine if the shear strain is zero.

In conclusion, to accurately calculate the transverse loading for the beam, you will need to have more information about the loading and beam properties. I recommend consulting a structural engineer or using a beam calculator to obtain more accurate results.