CE 201 Statics

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CE 201 - Statics

• Lecture 15

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Reduction of a Simple Distributed Loading

• In many cases, bodies or structures are subjected
  to distributed loading. The loading intensity at
  each point is measured in lb/ ft2 or N/m2 which
  are units of pressure. Uniform distributed
  loading will be discussed. If we have the
  distributed loading shown

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• The loading is a system of parallel forces. The
  number of forces is infinite and separated by
  differential distances. The loading function is
  a function of x
• p p (x)
• If p p (x) was multiplied by the width ( a
  ), the loading along y will be obtained
• w p (x) N/m2 a m w (x) N/m

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• The loading intensity is represented by a
  coplannar system of forces.

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Magnitude of Resultant Force

• To find the resultant force ( FR ? F ),
  integration must be followed since infinite
  number of forces (dF) are acting on the body.
• dF w(x) dx dA
• (since w(x) is the force per unit length, x)
• for the entire length,
• FR ? F
• ? w (x)
  dx ? dA A
• Therefore, the magnitude of the resultant force
  is equal to the entire area under the loading
  diagram w w(x) .

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Location of Resultant Force

• Using MR ? M
• The location of FR (D) is found by equating the
  moments of FR and distributed forces about point
  (O)
• D FR ? x w(x) dx
• Then, D ? x w(x) dx / FR
• Substituting for FR
• D ? x w(x) dx / ? w(x) dx
• ? x dA / ? dA
• which is the equation of the geometric center
  (centroid). Therefore, FR acts at the centroid
  of the distributed loading diagram

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