Beam equilibrium and shear force

In summary, the conversation discusses how transverse loads are applied to a beam and how to determine expressions for the transverse shear force and bending moment at different points along the beam. The problem also involves using equations and a free body diagram to find the solutions.
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Homework Statement


transverse loads are applied to the beam in the figure at A, C, and E, and a concentrated couple 3Pa is applied to the beam at E. Determine expressions for (a) the transverse shear force Vc and bending moment Mc at a section just to the left of the load at C, and (b) shear Vd and moment Md just to the left of the support at D. Express answers in terms of P and a.

The image is the same setup as this problem only the loads at A, C and E are P, 2P and 2P respectively
p5.2-03alt.gif


Homework Equations


I know that the derived equations are V=dM/dx and p(x)=dV/dx but I don't really know how to go about doing this. I have my free body diagram but other than that I don't know where to start. Can anyone give me a hand?


The Attempt at a Solution

 
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  • #2
Start with point A. What's the shear force there? Does it change between points A and B? What happens to the shear force at point B?
 

1. What is beam equilibrium?

Beam equilibrium is the state in which the forces acting on a beam are balanced, resulting in no net force or moment acting on the beam. This means that the beam will remain stationary and not experience any deformation or movement.

2. How is beam equilibrium achieved?

Beam equilibrium is achieved by ensuring that the sum of the forces and moments acting on the beam are equal to zero. This can be achieved by properly designing and distributing the loads and supports on the beam.

3. What is shear force in a beam?

Shear force is the internal force that causes a portion of the beam to slide or shear in relation to another portion of the beam. It is typically represented by the symbol V and is measured in Newtons (N) or pounds (lbs).

4. How is shear force calculated?

Shear force can be calculated by taking the sum of the vertical forces acting on a particular section of the beam. This section is known as a "cut section" and the shear force at that section is equal to the sum of the forces acting on either side of the cut section.

5. What is the relationship between beam equilibrium and shear force?

In order to achieve beam equilibrium, the shear force must be equal to zero at all points along the beam. This means that the forces acting on the beam must be balanced in order for the beam to remain stationary and not experience any deformation.

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