For a beam fixed at both ends, what is the formula for the maximum deflection un

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Question: For a beam fixed at both ends, what is the formula for the maximum deflection under a central point load?

Options:

Correct Answer: PL^3/12EI

Solution:

The maximum deflection (δ) for a beam fixed at both ends under a central point load (P) is given by δ = PL^3/12EI.

For a beam fixed at both ends, what is the formula for the maximum deflection under a central point load?

For a beam fixed at both ends, what is the formula for the maximum deflection under a central point load?

Step 1: Understand the problem. We have a beam that is fixed at both ends and we want to find out how much it bends (deflects) when a weight (point load) is placed in the middle.
Step 2: Identify the variables in the formula. The formula for maximum deflection involves the following variables: P (the point load), L (the length of the beam), E (the modulus of elasticity of the material), and I (the moment of inertia of the beam's cross-section).
Step 3: Write down the formula for maximum deflection. The formula is δ = PL^3 / 12EI.
Step 4: Understand what each part of the formula means. 'P' is the force applied at the center, 'L' is how long the beam is, 'E' is a measure of how stiff the material is, and 'I' is a measure of how the shape of the beam affects its bending.
Step 5: Use the formula to calculate the maximum deflection if you know the values of P, L, E, and I.

Beam Deflection – The study of how beams deform under loads, specifically focusing on maximum deflection in this case.
Fixed Beam Conditions – Understanding the boundary conditions of a beam fixed at both ends, which affects its deflection characteristics.
Load Types – Recognizing the impact of a central point load on the deflection of beams.
Material Properties – The role of the modulus of elasticity (E) and moment of inertia (I) in determining beam deflection.