ME 201 Engineering Mechanics: Statics

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ME 201Engineering Mechanics Statics

• Chapter 4 Part D
• 4.10 Distributed Loading

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Distributed Loads

• Thus far weve been working with loads that are
  concentrated at a point
• Many times in engineering we need to be concerned
  with another type of loading referred to as
  distributed loading

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Distributed Loads

• To compute the resultant, FR, of a distributed
  load, consider the following
• To find FR, we need to sum an infinite number of
  small forces

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Distributed Loads

• Consider a small differential element, dF, with a
  width of dx and a height of w(x)
• The area of the element is
• Since infinite number of forces, need to integrate

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Distributed Loads

• Where does FR act?
• Can be determined by equating the moments of the
  force resultant and the force distribution

This is also the centroid of the area
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Centroids

• For simple shapes, centroid can be found in a
  table (see back cover of textbook)
• Where is the centroid for these common shapes?

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Example Problem

• Given
• w400 lb/ft
• Find
• FR,

w lb/ft
A
B
10 ft
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Example Problem Solution
w lb/ft

• Given
• w400 lb/ft
• Find
• FR,

A
B
10 ft
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Example Problem

• Given
• w100x N/m
• Find
• FR,

600 N/m
A
B
6 m
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Example Problem Solution
600 N/m

• Given
• w100x N/m
• Find
• FR,

A
B
6 m
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Example Problem
100 lb/ft

• Given
• trapezoid
• Find
• FR,

50 lb/ft
A
B
9 ft
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Example Problem Solution
100 lb/ft

• Given
• trapezoid
• Find
• FR,

50 lb/ft
A
B
9 ft
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Example Problem

• Given
• trapezoid
• Find
• FR,

W60x2 N/m
2 m
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Example Problem Solution

• Given
• trapezoid
• Find
• FR,