Chapt 4. Shear forces

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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?

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4.2 general method

• Notation of internal force moments

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• sign convention ? ??? ??

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• 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)

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Ex 4.1)

• Internal force moments at C?

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?)
a
b
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Ex 4.2)

• V M at C1, C2?

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• ?)

x
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Ex 4.3)

• Shear force, axial force, bending moment at
  section C?

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• ?)

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Ex 4.4)

• V, N M at C ?

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• ?)

VA
VA
RA
n
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4.3 shear force bending moments diagrams

• V
• plotted along x
• M

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Ex 4.5)

• V-x M-x ? ?

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• ?)

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Ex 4.6)
P50kN, a3m, L14m
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?)
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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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?)
?
?
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Ex 4.8)

• SFD BMD?

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?)

• w? resultant force

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Ex 4.9)
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?) 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
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?
(?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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?)
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using (?1) (?2)
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Ex 4.11) SFD BMD?
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At a small element A
(?1) ?
(?2) ?
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Ex 4.12) SFD BMD
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From equil.?
For AB
(?1) ?
(?2) ?
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For BC
(?1) ?
(?2) ?
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Ex 4.13)
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? (?1)
Ex 4.14)
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Ex 4.15)
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?)
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