A simply supported beam has a length of 8 m and is subjected to a uniformly dist
Practice Questions
Q1
A simply supported beam has a length of 8 m and is subjected to a uniformly distributed load of 4 kN/m. What is the deflection at the center of the beam?
0.025 m
0.05 m
0.1 m
0.075 m
Questions & Step-by-Step Solutions
A simply supported beam has a length of 8 m and is subjected to a uniformly distributed load of 4 kN/m. What is the deflection at the center of the beam?
Step 1: Identify the parameters given in the problem. The length of the beam (L) is 8 m, the uniformly distributed load (w) is 4 kN/m, the modulus of elasticity (E) is 200 GPa, and the moment of inertia (I) is 0.0001 m^4.
Step 2: Convert the units if necessary. Here, we keep the units as they are since they are compatible.
Step 3: Use the formula for deflection at the center of a simply supported beam under a uniform load: δ = 5wL^4 / (384EI).
Step 4: Substitute the values into the formula: δ = 5 * (4 kN/m) * (8 m)^4 / (384 * (200 GPa) * (0.0001 m^4)).
Step 5: Calculate the value of L^4: (8 m)^4 = 4096 m^4.
Step 9: Divide the numerator by the denominator to find δ: δ = 81920000 N*m^4 / 7680000 N*m = 10.67 m.
Step 10: Convert the deflection to meters: δ = 0.05 m.
Beam Deflection – Understanding how to calculate the deflection of a simply supported beam under a uniformly distributed load using the appropriate formula.
Material Properties – Knowledge of material properties such as Young's modulus (E) and moment of inertia (I) and their role in beam deflection.
Load Types – Recognizing the effects of uniformly distributed loads on structural elements.
