[Statics] Determining the normal force at an internal point of a member

In summary, the correct way to find the normal force at point E is to divide the frame into members AB and CB, solve for the x and y components of the reaction force at point B, and use a free body diagram to set the sum of the x-components of the forces to 0 and solve for the normal force. However, treating the two members as a system and solving for the x-component of the reaction force at point C does not give the same answer. This discrepancy may be due to using the wrong number in the second method.
  • #1
Worn_Out_Tools
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TL;DR Summary
A statics question regarding a two-member frame.
For this problem (see image), I get the correct answer for the normal force at point E if I:
1) divide the frame into members AB and CB,
2) solve for the x and y components of the reaction force at point B,
3) make a free body diagram with the cut at point E forming member EB and setting the sum of the x-components of the forces to 0 and solving for the normal force.

BUT

If I try to solve it by treating the two members as a system (and, thus, discount the reaction force at B), setting the sum of the moments about point A to 0 and then solving that for the x-component of the reaction force at point C which would then equal the the negative of the normal force at point E, I don't get the same answer. Why is that?
 

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  • #2
I figured it out. Used a wrong number for the second method causing the answer to differ. Thank you nonetheless.
 
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1. What is the normal force in statics?

The normal force in statics is the force that is perpendicular to the surface of an object. It is responsible for supporting the weight of an object and preventing it from falling through a surface.

2. How is the normal force calculated?

The normal force can be calculated using the formula FN = mg cos(theta), where FN is the normal force, m is the mass of the object, g is the acceleration due to gravity, and theta is the angle between the surface and the direction of gravity.

3. What is the significance of determining the normal force at an internal point of a member?

Determining the normal force at an internal point of a member is important in understanding the overall stability and equilibrium of a structure. It allows engineers to ensure that the structure can support the expected load without collapsing or failing.

4. What factors affect the normal force at an internal point of a member?

The normal force at an internal point of a member is affected by the weight of the object, the angle of the surface, and the external forces acting on the object. It can also be influenced by the material properties of the member, such as its stiffness and elasticity.

5. How can the normal force at an internal point of a member be measured?

The normal force at an internal point of a member can be measured using a force sensor or load cell. These devices can be placed at the point of interest to accurately measure the force acting on the member. Alternatively, the normal force can also be calculated using the equations of equilibrium and known external forces.

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