What is the deflection formula for a simply supported beam with a point load at the center?
Practice Questions
1 question
Q1
What is the deflection formula for a simply supported beam with a point load at the center?
(P * L^3) / (48 * E * I)
(P * L^3) / (3 * E * I)
(P * L^3) / (12 * E * I)
(P * L^2) / (2 * E * I)
The deflection (δ) at the center of a simply supported beam with a point load (P) at the center is given by δ = (P * L^3) / (48 * E * I), where E is the modulus of elasticity and I is the moment of inertia.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the deflection formula for a simply supported beam with a point load at the center?
Solution: The deflection (δ) at the center of a simply supported beam with a point load (P) at the center is given by δ = (P * L^3) / (48 * E * I), where E is the modulus of elasticity and I is the moment of inertia.
Steps: 6
Step 1: Understand that a simply supported beam is supported at both ends and can bend in the middle.
Step 2: Recognize that a point load (P) is a force applied at a single point, in this case, at the center of the beam.
Step 3: Identify the length of the beam as L, which is the distance between the two supports.
Step 4: Know that E represents the modulus of elasticity, which measures how much the material will deform under stress.
Step 5: Understand that I is the moment of inertia, which is a property of the beam's cross-section that affects its stiffness.
Step 6: Use the deflection formula: δ = (P * L^3) / (48 * E * I) to calculate the deflection at the center of the beam.
