Determine the shear-force and bending-moment equations for the beam?

[ChangBroot]

Determine the shear-force and bending-moment equations for the beam. Then sketch the
diagrams using the aforementioned equations if necessary to ascertain key points in the
diagrams, such as the position between the supports where V=0. What is the bending
moment there?

The following is the figure and how I drew the Free Body Diagram. Remember, I only neglected the Coupled-Forces, not the m0ment they cause.

http://s1267.beta.photobucket.com/user/ChangBroot/media/ShearForceandBendingMoment-1.png.html

I found:
W = 180 N
Ay = 60 N
By = 1120 N

No need for the sketching part, I can do that. Just need help with the equations.

Any help is greatly appreciated.

 

[SteamKing]

By their nature, simple supports can transmit forces but are incapable of transmitting any moments.

What specific problems are you having with the equations?

 

[ChangBroot]

I am having difficulty finding ".. the shear-force and bending-moment equations for the beam. "

 

[SteamKing]

What have you tried? Have you started to write anything down?

 

[alphy]

I would approach this problem by first identifying the key variables and principles involved. In this case, we are dealing with a beam under external forces, so we can use the principles of statics to determine the shear-force and bending-moment equations.

To start, we need to draw a free body diagram of the beam, as shown in the figure provided. This will help us visualize the forces acting on the beam and determine the equations needed.

The shear-force equation can be determined by considering the vertical forces acting on the beam. In this case, we have two forces acting in the upward direction (Ay and By) and one force acting downward (W). Since the beam is in equilibrium, the sum of all vertical forces must equal zero. This leads to the equation: Ay + By - W = 0.

Next, we can determine the bending-moment equation by considering the moments around a point on the beam. We can choose any point, but it is often helpful to choose a point where some of the forces are known or where the bending-moment is zero. In this case, we can choose the left support as our reference point. The bending-moment equation can then be written as: M = Ay(x) + By(x) - W(x - L), where x is the distance from the left support and L is the length of the beam.

To find the position between the supports where V=0, we can set the shear-force equation equal to zero and solve for x. This will give us the point where the shear-force changes direction, which is also the point where the bending-moment is zero. In this case, we have: Ay + By - W = 0, which leads to x = L/2.

At this point, we can also determine the bending moment at this location by plugging in x = L/2 into the bending-moment equation. This will give us the bending moment at the midpoint of the beam, which is equal to Ay(L/2) + By(L/2) - W(L/2 - L). Simplifying this equation, we get: M = (Ay + By - W)L/2.

In summary, to determine the shear-force and bending-moment equations for a beam, we need to draw a free body diagram, apply the principles of statics, and solve for the unknown variables. By setting the shear-force equation equal to zero, we can find the point where