1. A simply supported beam AB of span 4 m is carrying a point loads of 5, 2 and 3 kN at 1, 2 and 3 m respectively from the support A. Calculate the reactions at the supports A and B. [Ans. 5.5 kN and 4.5 kN]
1. A simply supported beam AB of span 4 m is carrying a point loads of 5, 2 and 3 kN at 1, 2 and 3 m respectively from the support A. Calculate the reactions at the supports A and B. [Ans. 5.5 kN and 4.5 kN]
Question
![Note: In the second method, the uniformly distributed load between A and C will cause anticlockwise
moment about C, while the load between C and B will cause clockwise moment. But for the sake of simplicity, we
have taken the entire load from A to B (equal to 0.6 × 5) acting at its centre (i.e. 2.5 m from A or 2.5 - x) from C.
EXERCISE 12.1
1. A simply supported beam AB of span 4 m is carrying a point loads of 5, 2 and 3 kN at 1, 2
and 3 m respectively from the support A. Calculate the reactions at the supports A and B.
[Ans. 5.5 kN and 4.5 kN]
2. A simply supported beam of span 6 m is carrying a uniformly distributed load of 2 kN/m
over a length of 3 m from the right end B. Calculate the support reactions.
[Ans. R = 1.5 kN, R, = 4.5 kN]
3. A simply supported beam AB of span 6 m is loaded as shown in Fig. 12.14.
2 kN
5 kN
2 kN/m
2 kN/m
+1.5 m→
A
В
E
3 m
D
+1.5 m-
6 m
Fig. 12.14.
Determine the reactions at A and B.
[Ans. 6.875 kN, 9.125 kN]
226 I A Textbook of Engineering Mechanics
4. A beam AB6 m long rests on two supports 4 m apart, the right hand end is overhanging
by 2 m. The beam carries a uniformly distributed load of 1 kN/m over the entire length
of the beam.
Determine the reactions at the two supports.
[Ans. R = 1.5 kN, R„= 4.5 kN]
5. A beam ABCDEF of 7.5 m long and span 4.5 m is supported at B and E. The beam is
loaded as shown in Fig. 12.15.
5 kN
-9 kN/m
3 kN/m
A
B
+1.5m 1.5m-
E
1.5 m→
+1.8m
4.5 m
Fig. 12.15.
Find graphically, or otherwise, the support reactions at the two supports.
[Ans. R3 = 29.33 kN, R; = 12.57 kN]
6. A beam ABCDE hinged at A and supported on rollers at D, is loaded as shown in Fig. 12.16.
6 kN
3 kN
1 kN/m
30°
В
+ 2 m + 2 m→
4 m
1 m
Fig. 12.16.
Find the reactions at A and D.
[Ans. R = 5.94 kN, R, = 7.125 kN, 0 = 61°]
12.14. ROLLER SUPPORTED BEAMS
In such a case, the end of a beam is supported on rollers, and the reaction on such an end is
always normal to the support, as shown in Fig. 12.17 (a) and (b). All the steel trusses, of the bridges,
have one of their ends as supported on rollers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febe67c62-cc49-4b28-af1f-e41019fe1942%2Fc6901cdb-7a69-4aa6-829c-34a560630df6%2Fwmlly2p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Note: In the second method, the uniformly distributed load between A and C will cause anticlockwise
moment about C, while the load between C and B will cause clockwise moment. But for the sake of simplicity, we
have taken the entire load from A to B (equal to 0.6 × 5) acting at its centre (i.e. 2.5 m from A or 2.5 - x) from C.
EXERCISE 12.1
1. A simply supported beam AB of span 4 m is carrying a point loads of 5, 2 and 3 kN at 1, 2
and 3 m respectively from the support A. Calculate the reactions at the supports A and B.
[Ans. 5.5 kN and 4.5 kN]
2. A simply supported beam of span 6 m is carrying a uniformly distributed load of 2 kN/m
over a length of 3 m from the right end B. Calculate the support reactions.
[Ans. R = 1.5 kN, R, = 4.5 kN]
3. A simply supported beam AB of span 6 m is loaded as shown in Fig. 12.14.
2 kN
5 kN
2 kN/m
2 kN/m
+1.5 m→
A
В
E
3 m
D
+1.5 m-
6 m
Fig. 12.14.
Determine the reactions at A and B.
[Ans. 6.875 kN, 9.125 kN]
226 I A Textbook of Engineering Mechanics
4. A beam AB6 m long rests on two supports 4 m apart, the right hand end is overhanging
by 2 m. The beam carries a uniformly distributed load of 1 kN/m over the entire length
of the beam.
Determine the reactions at the two supports.
[Ans. R = 1.5 kN, R„= 4.5 kN]
5. A beam ABCDEF of 7.5 m long and span 4.5 m is supported at B and E. The beam is
loaded as shown in Fig. 12.15.
5 kN
-9 kN/m
3 kN/m
A
B
+1.5m 1.5m-
E
1.5 m→
+1.8m
4.5 m
Fig. 12.15.
Find graphically, or otherwise, the support reactions at the two supports.
[Ans. R3 = 29.33 kN, R; = 12.57 kN]
6. A beam ABCDE hinged at A and supported on rollers at D, is loaded as shown in Fig. 12.16.
6 kN
3 kN
1 kN/m
30°
В
+ 2 m + 2 m→
4 m
1 m
Fig. 12.16.
Find the reactions at A and D.
[Ans. R = 5.94 kN, R, = 7.125 kN, 0 = 61°]
12.14. ROLLER SUPPORTED BEAMS
In such a case, the end of a beam is supported on rollers, and the reaction on such an end is
always normal to the support, as shown in Fig. 12.17 (a) and (b). All the steel trusses, of the bridges,
have one of their ends as supported on rollers.
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