Engineering Science Simply Supported Beams answers
2. A light beam is supported and loaded as shown in the diagram. Draw the shear force and bending moment diagrams and determine the size and position of the maximum bending moment and maximum shear force.
2 m
60 kN
3 m
A
R
1
C
R
1
= 36 kN R
2
= 24 kN
R
2
B
36 kN
0
A C B
-24 kN
72 kNm
A
C
B
4. A light beam is supported and loaded as shown in the diagram. Draw the shear force and bending moment diagrams and determine the size and position of the maximum bending moment and maximum shear force.
A
R
1
8 kN
2 m
R
1
= 5.6 kN R
5.6 kN
2
= 6.4 kN
0
A
11.2 kNm
C
6.4 kNm
0
A C
2 m
4 kN
D
D
1 m
R
2
-2.4 kN
B
B
-6.4 kN
B
5. A light beam is supported and loaded as shown in the diagram. Draw the shear force and bending moment diagrams and determine the size and position of the maximum bending moment and maximum shear force.
2 m
40 kN
1 m 2 m
5 kN
A
R
1
R
1
= 10 kN R
2
= 35 kN
R
2
B
10 kN
0
A B
5 kN
20 kNm
-30 kN
A
-10 kNm
B
7. Draw shear force and bending moment diagrams for a uniform beam of total weight 60 kN which is supported as shown.
A
R
1
15 kNm
3 m
-1
R
2
1 m
B
R
2
= 40 kN R
1
= 20 kN
20 kN
15 kN
13.3 kNm
-25 kN
-7.5 kNm
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Engineering Science Simply Supported Beams answers
8. An additional uniformly distributed load of total weight
10 kN is added to the beam of question 4 as shown in the diagram below. Draw shear force diagram for new loading.
8 kN
2 m 2 m
4 kN
1 m
A
R
1
R
1
= 9.6 kN R
2
= 12.4 kN
9.6 KN
R
2
B
1.6 KN
-8.4 KN
-12.4 KN
9. The diagram shows a simply-supported beam loaded with point and distributive forces.
Calculate the reactions R
1
and R
2
Construct a shear force diagram
Determine the maximum bending moment and state where it occurs
1kN/m run
2 kN 2 kN
2 m
R
1
= 8 kN
R
1
R
2
4 m
= 4 kN
2 m 2 m 2 m
R
2
0
6 kN
2 kN
0
-2 kN
-2 kN
-4 kN
Maximum bending occurs where the shear force is zero (ie where it cuts zero line on diagram)
This occurs at 2 m from the left hand end or 6 m from the left hand end.
BM
2
= (2x4) + (2x8) + (1x6x3) – (4x10) = 2kNm
[ To the right BM
2
= (1x2x1) = 2kNm ]
BM
6
= (2x4) + (1x2x1) – (4x6) = -14kNm
[ To the right BM
2
= -(4x8) + (1x6x3) = -14kNm ]
10. Draw the shear force and bending moment diagrams for the light beam which is loaded as shown in the diagram.
2 kN
3 kN 4 kN 1 kN
1 m
+4
R
-2
1
-2
1 m
+1
+2
2 m
-3
+4
2 m
+1
-2
R
2
2 m
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