How Do You Calculate Stress at Different Points in a Loaded Beam?

[Junkwisch]

Homework Statement

"see attachment"Normally I would assume that the stress caused by the point load at A is equal to σ=P/Area. however since there is a distance between the two points and because of Saint Venants principle, I don't think that the stress at A will be the same with the stress at D. In order to find the stress at D, do I have to find the centroid or the moment? (using this equation σ=((-My)/I) ) or angle of twist??

 

[SteamKing]

Well, the attachment is not totally clear on the position of A, but let's assume that the force at A is applied at the center of the cross-section.

Why would you assume that a centrally loaded member has developed a bending moment?

What is it about this problem which makes you think St. Venant's principle applies?

You've got a prismatic member with a square cross-section. Can't you identify the location of the centroid without calculation?

 

[Junkwisch]

I don't think that there will be any moment in the center load. (Can I assume that the stress will be exactly the same for the entire rectangle?)

For the St. Venants principle, I think it is there because point D is on the side of the rectangle, i doubt that it will experience the same stress as that of the centre of the rectangle.

The centroid should be in the centre of the rectangle.

 

[SteamKing]

I don't think that there will be any moment in the center load. (Can I assume that the stress will be exactly the same for the entire rectangle?)

For the St. Venants principle, I think it is there because point D is on the side of the rectangle, i doubt that it will experience the same stress as that of the centre of the rectangle.

The centroid should be in the centre of the rectangle.

Well, axial loads are assumed to produce the same stress over the entire cross-section. After all, that's what σ = P/A means.

 

[rezeew]

I would first commend you on thinking critically about the problem and considering the principles of Saint Venants. You are correct in thinking that the stress at point A will not be the same as the stress at point D due to the distance between them and the principle of Saint Venants.

To calculate the stress at point D, you will need to consider the centroid and moment of the load. The equation you mentioned, σ=((-My)/I), is known as the flexural stress equation and can be used to calculate the stress at a point due to a bending moment. However, in this case, you will also need to consider the axial stress caused by the point load at A.

To accurately calculate the stress at D, you will need to use a combination of equations, such as the flexural stress equation and the axial stress equation (σ=P/A). You may also need to consider the angle of twist, depending on the specific problem. It is important to carefully consider all the factors at play and use the appropriate equations to accurately calculate the resultant stress at point D.

I would also recommend consulting with a structural engineer or referring to a textbook for more guidance on how to approach this problem. As a scientist, it is important to always use accurate and reliable methods to solve problems and make conclusions.