Conditions for Equilibrium

In summary, if there is a cross member of a bridge with two forces (F and R) acting as contacts at the ends of the member, the equilibrium conditions must be satisfied (Fy and Ry are equal and opposite, Fx and Rx are equal and opposite). If the member is a 2-force member, then Fy/Fx = Ry/Rx = tan theta. If the weight of the member is significant, it can be split and applied to the adjacent joints, but this may introduce shear loads in addition to axial loads.
  • #1
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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  • #2
drawing a FBD would help us interpret the problem
 
  • #3
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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  • #4
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.
 

What is equilibrium?

Equilibrium is a state of balance or stability in a system, where the forces acting on the system are equal and opposite, resulting in a lack of net change.

What are the conditions for equilibrium?

The conditions for equilibrium include the absence of any net force acting on the system, as well as the absence of any net torque or rotational force. In other words, the sum of all the forces and torques acting on the system must be equal to zero for equilibrium to be achieved.

How is equilibrium achieved?

Equilibrium is achieved when the forces and torques acting on a system are balanced, resulting in a state of no net change. This can be achieved by adjusting the magnitude and direction of the forces and torques until they cancel each other out.

What is the difference between static and dynamic equilibrium?

Static equilibrium is a state where a system is at rest and does not experience any change in motion or position, while dynamic equilibrium is a state where a system is in motion but experiences no net change in its speed or direction.

What are some real-life examples of equilibrium?

Some real-life examples of equilibrium include a book sitting on a table (static equilibrium), a car traveling at a constant speed on a straight road (dynamic equilibrium), and a seesaw with equal weights on both sides (rotational equilibrium).

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