A 16 kN/m 80 kN.m 75 kN B 2 m 2 m 1 m 2 m 5 m El is constant all across the structure. A) Find X1 D Use the Force Method to analyse the beam shown in the Figure by introducing hinges and corresponding redundant bending moments at points A, B, C. Plot the bending moment (M) and shear force (V) diagrams for the loading shown. associated with the unit moment at A. B) Find X2. Note: X2 is associated with the unit moment at B. C) Find X3. Note: X3 is associated with the unit moment at C. D) Based on X1, X2, and X3: Find Ray (Vertical reaction at A) E) Based on X1, X2, and X3: Find RDy (Vertical reaction at D) - X1 is Hints to help you proceed First draw the BMD of Mo, M1, M2, M3. Then, develop the matrix and find X1, X2, and X3. Then, using the FBDs on the bottom of the page, find the shear components. A Mo MI A 1 X1 16 kN/m 5 m B 5 m B 16 kN/m VAB 80 kN.m 75 kN D M2 Ар 2 m 2 m 1 m 2 m VBA 4 m 3 m D M3 A B 5 m 4 m 3 m 5 m 80 kN.m X2 X2 X3 X3 VCB VBC B 3 m 4 m 75 kN VDC VCD D D
A 16 kN/m 80 kN.m 75 kN B 2 m 2 m 1 m 2 m 5 m El is constant all across the structure. A) Find X1 D Use the Force Method to analyse the beam shown in the Figure by introducing hinges and corresponding redundant bending moments at points A, B, C. Plot the bending moment (M) and shear force (V) diagrams for the loading shown. associated with the unit moment at A. B) Find X2. Note: X2 is associated with the unit moment at B. C) Find X3. Note: X3 is associated with the unit moment at C. D) Based on X1, X2, and X3: Find Ray (Vertical reaction at A) E) Based on X1, X2, and X3: Find RDy (Vertical reaction at D) - X1 is Hints to help you proceed First draw the BMD of Mo, M1, M2, M3. Then, develop the matrix and find X1, X2, and X3. Then, using the FBDs on the bottom of the page, find the shear components. A Mo MI A 1 X1 16 kN/m 5 m B 5 m B 16 kN/m VAB 80 kN.m 75 kN D M2 Ар 2 m 2 m 1 m 2 m VBA 4 m 3 m D M3 A B 5 m 4 m 3 m 5 m 80 kN.m X2 X2 X3 X3 VCB VBC B 3 m 4 m 75 kN VDC VCD D D
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A
16 kN/m
80 kN.m
75 kN
B
2 m
2 m 1 m
2 m
5 m
El is constant all across the structure.
A) Find X1
D
Use the Force Method to analyse the beam shown in the Figure
by introducing hinges and corresponding redundant bending
moments at points A, B, C. Plot the bending moment (M) and
shear force (V) diagrams for the loading shown.
associated with the unit moment at A.
B) Find X2. Note: X2 is associated with the unit moment at B.
C) Find X3. Note: X3 is associated with the unit moment at C.
D) Based on X1, X2, and X3: Find Ray (Vertical reaction at A)
E) Based on X1, X2, and X3: Find RDy (Vertical reaction at D)
- X1 is
Hints to help you proceed
First draw the BMD of Mo, M1, M2, M3. Then, develop the matrix and find X1, X2, and X3. Then, using the FBDs on the
bottom of the page, find the shear components.
A
Mo
MI A
1
X1
16 kN/m
5 m
B
5 m
B
16 kN/m
VAB
80 kN.m
75 kN
D
M2
Ар
2 m
2 m
1 m 2 m
VBA
4 m
3 m
D
M3 A
B
5 m
4 m
3 m
5 m
80 kN.m
X2
X2
X3
X3
VCB
VBC
B
3 m
4 m
75 kN
VDC
VCD
D
D
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