For a fixed beam subjected to a point load at the center, what is the ratio of t

For a fixed beam subjected to a point load at the center, what is the ratio of the maximum moment to that of a simply supported beam?

For a fixed beam subjected to a point load at the center, what is the ratio of the maximum moment to that of a simply supported beam?

Step 1: Understand the types of beams. A fixed beam is supported at both ends and cannot rotate, while a simply supported beam can rotate at its supports.
Step 2: Identify the load. In this case, there is a point load applied at the center of both beams.
Step 3: Calculate the maximum moment for a simply supported beam. The formula for the maximum moment (M) in a simply supported beam with a point load (P) at the center is M = P * L / 4, where L is the length of the beam.
Step 4: Calculate the maximum moment for a fixed beam. The formula for the maximum moment in a fixed beam with the same point load at the center is M = P * L / 8.
Step 5: Find the ratio of the maximum moments. To find the ratio of the maximum moment in the fixed beam to that in the simply supported beam, divide the fixed beam moment by the simply supported beam moment: Ratio = (P * L / 8) / (P * L / 4).
Step 6: Simplify the ratio. The P and L cancel out, leaving Ratio = (1/8) / (1/4) = 1/2.
Step 7: Invert the ratio to express the fixed beam moment in terms of the simply supported beam moment. Since the maximum moment in the fixed beam is twice that of the simply supported beam, the ratio is 2.

Bending Moment – Understanding how bending moments differ in fixed and simply supported beams under point loads.
Beam Support Conditions – Knowledge of how different support conditions (fixed vs. simply supported) affect the structural response.
Structural Analysis – Application of principles of structural analysis to determine moments in beams.