Answer :
The deflection at point C is ________ (Option c).
To calculate the deflection at point C using the Moment-Area Method, we follow these steps:
1. Determine the maximum bending moment (Mₘₐₓ) caused by the applied load and any additional moments.
Given:
P = 5 k (applied load)
a = 3 ft (distance from the load to point C)
Using the equation for a simply supported beam with a concentrated load at midspan, we find:
Mₘₐₓ = (P * a) / 2
= (5 * 3) / 2
= 7.5 k-ft
2. Construct the moment diagram to visualize the bending moment along the beam's length.
3. Determine the area under the moment diagram up to point C.
Since the beam is symmetric, we can calculate the area under the moment diagram up to point C by finding the area of the triangular region.
The area (A) of a triangle is given by the formula A = (1/2) * base * height.
Here, the base is the distance from point A to point C, which is 1.5 ft (half of the beam's length).
The height of the triangle is the maximum bending moment at point C, which is 7.5 k-ft.
Substituting the values, we get:
A = (1/2) * 1.5 * 7.5
= 5.625 k-ft²
4. Calculate the deflection using the formula δ = A / EI.
Given:
E = 29000 ksi
I = 76.8 in⁴
Convert the area from k-ft² to in⁴:
1 k-ft² = 12 * 12 * 1000 in⁴ = 144000 in⁴
Therefore, A = 5.625 * 144000 in⁴
= 810000 in⁶
Substituting the values into the deflection formula:
δ = A / EI
= (810000) / (29000 * 76.8)
≈ 3.68 inches
Therefore, the deflection at point C is approximately 3.68 inches.
Complete Question:
QUESTION: For the beam below, take P=5k, w=0klf, a=3ft. The beam is made of steel with E=29000-ksi and the moment of inertia I=76.8-in⁴. Use the Moment-Area Method to solve this problem. The deflection at which point is ________?
Options:
a) Point A
b) Point B
c) Point C
d) Point D
