Your Question:

A continuous beam ABC is shown in Figure below.

10kN/m

2m

Step By Step Answers with Explanation

Step 1: Analyze the beam's reactions

Sum of moments about point A:

-20 kN * 4 m + 20 kN.m + R_C * 8 m = 0

Step 2: Determine the bending moments

To calculate the bending moments along the beam, we'll utilize the load-deflection relationship for continuous beams:

• y is the deflection of the beam at point x

Since the beam is symmetrical, the bending moments at the mid-points of each span are equal. Let's denote the bending moment at the mid-point of span AB as M_B.

EI * d^4y/dx^4 = 0

for 6 m < x < 8 m:

for 2 m < x < 6 m:

M(x) = -20 kN * (x - 4 m)^2 / 2 + 40 kN

Step 3: Sketch the shear force and bending moment diagrams (SFD and BMD)

The SFD shows the variation of the shear force along the beam, while the BMD indicates the variation of the bending moment.