How is stress related to force and area in a solid body under equilibrium?

In summary, the concept being discussed is that internal stresses in a solid 3D body must sum to zero for the body to remain in equilibrium. This is demonstrated by the fact that if the body is bisected, the resultant surface integral must equal the sum of the forces (P1 and P2) removed from the original body. This can also be understood as the stress over an area (Delta A) being integrated to find the new force, which must be equal to the sum of P1 and P2 for equilibrium to be maintained.
  • #1
v_pino
169
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Why is it the integral of delta P that must equal P1 and P2 in the second diagram (half of the original body)? I thought it is simply that Delta P = (P4 + P3).
 

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  • #2
I don't really get what your asking? I think the diagram is basically just stating that internal stresses in a solid 3D body must sum to zero, if they do not then the body is exploding.
 
  • #3
It says that if you bisect the body, that is already in equilibrium, the resultant surface integral has to equal P1+P2, which were removed, for the body to stay in equilibrium. It would also be correct to say what you are saying, but I think the main idea was that the surface integral has to be equal to what was removed.
 
  • #4
So stress=force/area. Does it mean that if I find the stress over the area (Delta A) and integrate it with respect to Delta A, then I get the new force which is equal to the sum of P1 and P2?
 

FAQ: How is stress related to force and area in a solid body under equilibrium?

What is equilibrium in solid body?

Equilibrium in solid body refers to a state where all forces acting on a solid object are balanced, resulting in a state of rest or constant motion with no acceleration. In this state, the net force and torque on the object are both equal to zero.

How is equilibrium achieved in solid body?

Equilibrium in solid body is achieved when the sum of all external forces and torques acting on the object is equal to zero. This can be achieved through proper positioning and distribution of weight, as well as the use of support structures such as ropes, cables, and beams.

What is the difference between static and dynamic equilibrium in solid body?

In static equilibrium, the object is at rest and there is no change in its position or motion. In dynamic equilibrium, the object is in constant motion at a constant velocity, but the forces and torques acting on it are still balanced. This can occur for example, when an object is in free fall with a constant velocity.

How does the center of gravity affect equilibrium in solid body?

The center of gravity is the point at which the weight of an object can be considered to be concentrated. In order to achieve equilibrium, the center of gravity must be directly above the base of support. If the center of gravity falls outside of the base of support, the object will be unstable and will topple over.

What factors can disrupt equilibrium in solid body?

Equilibrium in solid body can be disrupted by the introduction of external forces or changes in the object's mass distribution. This can occur through actions such as pushing, pulling, or adding/removing weight from the object. Additionally, uneven surfaces or friction can also affect the object's equilibrium.

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