What is the role of Q and the source of moments in eccentric loading problems?

  • #1
morpheus343
29
4
Homework Statement
Stresses at a point in the crossection due to an axial load in the centroid.
Relevant Equations
Swain formula
1704966420313.png
1704966433531.png

If there is an axial load on G the centroid and i want to calculate the stresses at point B , I will calculate the moments at point B then use the stress formula. I am confused as to what y and z is in this case. I know that y and z are the coordinates of the point that i want to calculate the stress at. Is it the same as zB and yB?
 
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  • #2
How is the section anchored or restricted from movement induced by that axial force along the x axis?
What is Q representing?
What is the source of those moments?
 
  • #3
Lnewqban said:
How is the section anchored or restricted from movement induced by that axial force along the x axis?
What is Q representing?
What is the source of those moments?
1705041937307.png

For some reason i thought it's an eccentric loading problem but it's just σx=My*z/Iy due to P. Q axial force should not produce bending stresses only normal at point B of crossection.
 

FAQ: What is the role of Q and the source of moments in eccentric loading problems?

What is the role of Q in eccentric loading problems?

In eccentric loading problems, Q typically represents the first moment of area about the neutral axis. It is crucial in determining the shear stress distribution within a structural member. The value of Q helps in calculating the shear flow, which is essential for understanding how the load is transferred through the material.

How is Q calculated in eccentric loading problems?

Q is calculated as the product of the area of a section above (or below) the point where the shear stress is being calculated and the distance from the centroid of that area to the neutral axis. Mathematically, Q = A'y', where A' is the area of the section and y' is the distance from the centroid of A' to the neutral axis.

What is the source of moments in eccentric loading problems?

The source of moments in eccentric loading problems is the eccentricity of the applied load. When a load is applied at a point that is not along the centroidal axis of the structural member, it creates a moment. This moment causes bending and additional stresses within the member, which need to be accounted for in the design and analysis.

How does eccentric loading affect the stress distribution in a structural member?

Eccentric loading causes a non-uniform stress distribution within a structural member. The eccentricity introduces bending moments that result in both tensile and compressive stresses across the cross-section. This is in addition to any direct stresses caused by the axial load itself. The combined effect must be analyzed to ensure the structural member can safely withstand the applied loads.

Why is it important to consider Q and moments in the design of structural members under eccentric loading?

Considering Q and moments in the design of structural members under eccentric loading is crucial for ensuring structural integrity and safety. Ignoring these factors can lead to underestimating the stresses and deformations, potentially resulting in structural failure. Proper analysis helps in designing members that can adequately resist the combined effects of shear, bending, and axial forces.

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