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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
  • sym. cross section in-plane loading
  • ?in-plane
    deform.
  • Simply supported cantilever
  • distributed load concentrated load
  • (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
  • For distributed load,
  • define
  • Distributed load ? resultant force
  • reaction force ?
    ??? ??

21
Ex 4.7) uniformly distributed load
  • 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? ?? ??
Loading diagram ? S.F.D ? BMD
??
??
????
????
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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