What is the shear force at a section located at a distance 'x' from the left end

What is the shear force at a section located at a distance 'x' from the left end of a simply supported beam with a point load at the center?

What is the shear force at a section located at a distance 'x' from the left end of a simply supported beam with a point load at the center?

Step 1: Understand the setup. You have a simply supported beam with a point load (W) applied at the center.
Step 2: Identify the total length of the beam. Let's call it 'L'. The point load is located at L/2.
Step 3: Recognize that the beam is supported at both ends, which means it can only move vertically at the supports.
Step 4: When you look at a section of the beam at a distance 'x' from the left end, you need to determine how much force is acting on that section.
Step 5: The shear force (V) at that section is affected by the point load and the distance 'x'.
Step 6: Calculate the reaction forces at the supports. Since the load is at the center, each support will carry half the load: W/2.
Step 7: For the section at distance 'x', the shear force is the reaction force at the left support minus the load to the right of the section.
Step 8: The load to the right of the section is simply the point load (W) since it is located at the center (L/2).
Step 9: Therefore, the shear force at the section is V = (W/2) - (W/2 - x) = W/2 - x.

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