How Do Equilibrium Conditions Relate to Forces in a Bridge Member?

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Homework Help Overview

The discussion revolves around the equilibrium conditions of forces acting on a bridge member, specifically focusing on how these conditions relate to the forces at the ends of the member. The member is positioned at an angle with respect to the horizontal, and participants are exploring the implications of net force and net torque being zero.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the utility of drawing a free body diagram (FBD) to better interpret the problem. There are mentions of relationships between forces when considering the member as a two-force member and the implications of including the member's weight in the analysis.

Discussion Status

Some participants have provided insights into the relationships between the forces based on equilibrium conditions, while others express similar challenges in understanding the problem. The discussion is ongoing, with various interpretations being explored regarding the effects of the member's weight and the nature of the forces involved.

Contextual Notes

There is a mention of the customary approach to splitting the weight of the member when considering its center of mass, as well as the distinction between treating the member as a truss versus a frame with shear loads. This indicates that assumptions about the member's weight and loading conditions are under consideration.

student45
If there is a cross member of a bridge with two forces (F and R) acting as contacts at the ends of the member, is there a way to use equilibrium conditions to write the relationships between the forces? The member makes an angle theta with the horizontal (upward and to the right) and has a center of mass at its geometrical center, with the origion (O) chosen at the point where R is acting (on the left end of the member). I'm just not sure how to approach this. All I know is that net force and net torque are both equal to zero, but I have no idea where to go from here. Thanks.
 
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drawing a FBD would help us interpret the problem
 
I Have the same problem

Hey, I know that this post is from a while ago, but I have the same problem...

Attached is an FBD of the problem.
 

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Zipp425 said:
Hey, I know that this post is from a while ago, but I have the same problem...

Attached is an FBD of the problem.
If you ignore the weight of the member, the equilibrium conditions must be satisfied (Fy and Ry are equal and opposite, Fx and Rx are equal and opposite, and further, since the member is a 2-force member (axial loading only), then Fy/Fx = Ry/Rx = tan theta.

If the weight of the member, acting thru its c.m., is considered, it is often customary to split its weight half and half, and apply that value to the adjacent joints. You still get the same relationships of the forces.

If the weight of the member is significant and must be considered as it actually acts thru its c.m., you still get the same equilibrium relationships between F and R, but you no longer have the Fy/Fx = tan theta relationship, because you no longer have a pure truss, you have a frame with shear loads introduced as well as axial loads.
 

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