# Chapt 4. Shear forces - PowerPoint PPT Presentation

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## Chapt 4. Shear forces

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### Chapt 4. Shear forces & bending moments in beams 4.3 shear force & bending moments diagrams V plotted along x M 4.4 ... – PowerPoint PPT presentation

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Title: Chapt 4. Shear forces

1
Chapt 4. Shear forces bending moments in beams
• ????? ????? ???

2
4.1 Introduction
• Beam- a slender member under transverse load to
its longitudinal axis.
• Internal forces moments in beams?

3
4.2 general method
• Notation of internal force moments

4
• sign convention ? ??? ??

5
• General approach to determine the inter. force
moment
• 1. Idealize the actual problem
• 2. Use the equation of equil. to calculate any
unknown reaction or support forces.
• 3. Cut the member at a section of interest
• ?in-plane
deform.
• Simply supported cantilever
• (water pressure,weight)

6
Ex 4.1)
• Internal force moments at C?

7
?)
a
b
8
Ex 4.2)
• V M at C1, C2?

9
• ?)

x
10
Ex 4.3)
• Shear force, axial force, bending moment at
section C?

11
• ?)

12
Ex 4.4)
• V, N M at C ?

13
• ?)

VA
VA
RA
n
14
4.3 shear force bending moments diagrams
• V
• plotted along x
• M

15
Ex 4.5)
• V-x M-x ? ?

16
• ?)

17
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18
Ex 4.6)
P50kN, a3m, L14m
19
?)
20
• define
• Distributed load ? resultant force
• reaction force ?
??? ??

21
• SFD BMD?

22
?)
?
?
23
Ex 4.8)
• SFD BMD?

24
?)
• w? resultant force

25
Ex 4.9)
26
?) neglecting the weight of the beam
R
27
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28
4.4 differential equilibrium relation
• Consider a small element of a beam

Force moment on the element
29
?
(?1)
(?2)
30
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31
Integrating (?1) (?2)
S.F.D? ?? ??
??
??
????
????
32
Ex 4.10) SFD BMD?
33
?)
34
using (?1) (?2)
35
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36
Ex 4.11) SFD BMD?
37
At a small element A
(?1) ?
(?2) ?
38
Ex 4.12) SFD BMD
39
From equil.?
For AB
(?1) ?
(?2) ?
40
For BC
(?1) ?
(?2) ?
41
Ex 4.13)
42
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43
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44
? (?1)
Ex 4.14)
45
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46
Ex 4.15)
47
?)
48
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49
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