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Chapt 4. Shear forces bending moments in beams

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4.1 Introduction

- Beam- a slender member under transverse load to

its longitudinal axis. - Internal forces moments in beams?

4.2 general method

- Notation of internal force moments

- sign convention ? ??? ??

- 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)

Ex 4.1)

- Internal force moments at C?

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a

b

Ex 4.2)

- V M at C1, C2?

- ?)

x

Ex 4.3)

- Shear force, axial force, bending moment at

section C?

- ?)

Ex 4.4)

- V, N M at C ?

- ?)

VA

VA

RA

n

4.3 shear force bending moments diagrams

- V
- plotted along x
- M

Ex 4.5)

- V-x M-x ? ?

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Ex 4.6)

P50kN, a3m, L14m

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- For distributed load,
- define

- Distributed load ? resultant force
- reaction force ?

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Ex 4.7) uniformly distributed load

- SFD BMD?

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?

?

Ex 4.8)

- SFD BMD?

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- w? resultant force

Ex 4.9)

?) neglecting the weight of the beam

R

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4.4 differential equilibrium relation

- Consider a small element of a beam

Force moment on the element

?

(?1)

(?2)

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Integrating (?1) (?2)

S.F.D? ?? ??

Loading diagram ? S.F.D ? BMD

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Ex 4.10) SFD BMD?

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using (?1) (?2)

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Ex 4.11) SFD BMD?

At a small element A

(?1) ?

(?2) ?

Ex 4.12) SFD BMD

From equil.?

For AB

(?1) ?

(?2) ?

For BC

(?1) ?

(?2) ?

Ex 4.13)

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? (?1)

Ex 4.14)

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Ex 4.15)

?)

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