8 kN/m 6 kN/m 15 k 42 kN-m 6 k/ft 15 KN•M - 1.5 m- -3 m 30 kN 20 k-ft 9 kN 3 m 3 m- 9 kN V (kN) 4 ft 47 k 8k ft- w negative increasing V slope negative increasing w negative increasing V slope negative increasing w negative constant V slope negative constant V (kN) 4.5 -x (m) V (k) 32 Starts at- 9- 8 -x (m) zero slope -x (ft) 8 4 Ends at slope of -8 -30 -9 -15 V negative increasing M slope negative increasing V positive decreasing M slope positive decreasing M (kN-m) M (k•ft) М (kN-m) V negative increasing M slope negative increasing 15 18 Ends at 12 8 - slope of -9 Starts at zero slope -x (ft) Starts at 2.64 -20 slope of +9 х (m) Ends at -x (m) 1.5 3 slope of +8 Starts at (a) slope of – 15 -80 (c) Ends at slope of – 30 -42 (b)

8 kN/m 6 kN/m 15 k 42 kN-m 6 k/ft 15 KN•M - 1.5 m- -3 m 30 kN 20 k-ft 9 kN 3 m 3 m- 9 kN V (kN) 4 ft 47 k 8k ft- w negative increasing V slope negative increasing w negative increasing V slope negative increasing w negative constant V slope negative constant V (kN) 4.5 -x (m) V (k) 32 Starts at- 9- 8 -x (m) zero slope -x (ft) 8 4 Ends at slope of -8 -30 -9 -15 V negative increasing M slope negative increasing V positive decreasing M slope positive decreasing M (kN-m) M (k•ft) М (kN-m) V negative increasing M slope negative increasing 15 18 Ends at 12 8 - slope of -9 Starts at zero slope -x (ft) Starts at 2.64 -20 slope of +9 х (m) Ends at -x (m) 1.5 3 slope of +8 Starts at (a) slope of – 15 -80 (c) Ends at slope of – 30 -42 (b)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Bending Moment

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

Question

Draw the shear and moment diagrams for each of the beams shown.

8 kN/m
6 kN/m
15 k
42 kN-m
6 k/ft
15 KN•M
- 1.5 m-
-3 m
30 kN
20 k-ft
9 kN
3 m
3 m-
9 kN
V (kN)
4 ft
47 k
8k
ft-
w negative increasing
V slope negative increasing
w negative increasing
V slope negative increasing
w negative constant
V slope negative constant
V (kN)
4.5
-x (m)
V (k)
32
Starts at-
9-
8
-x (m)
zero slope
-x (ft)
8
4
Ends at
slope of -8
-30
-9
-15
V negative increasing
M slope negative increasing
V positive decreasing
M slope positive decreasing
M (kN-m)
M (k•ft)
М (kN-m)
V negative increasing
M slope negative increasing
15
18
Ends at
12
8
- slope
of -9
Starts at
zero slope
-x (ft)
Starts at
2.64
-20
slope
of +9
х (m)
Ends at
-x (m)
1.5
3
slope of +8
Starts at
(a)
slope of – 15
-80
(c)
Ends at
slope of – 30
-42
(b)

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