distributed forces
TRANSCRIPT
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Group 4
DISTRIBUTEDFORCES
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For all practical purposes these lines of action will be concurrent at a single point G, which is called the center of gravity of the body.
CENTERS OF MASS
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1. Lines
CENTROIDS OF LINES, AREAS, AND VOLUMES
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2. Areas
CENTROIDS OF LINES, AREAS, AND VOLUMES
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3. Volumes
CENTROIDS OF LINES, AREAS, AND VOLUMES
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AREA
When the density of ƥ is small but has constant thickness t, we can model it as surface area of A. so the mass of the element become
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Again, if ƥ and t are constant over the entire area, the coordinates of the center of mass of the body also become the coordinates of the centroid C of the surface area. The coordinates may be written
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EXAMPLE QUESTION
Determine the distance h from the base of triangle of altitude h to the centroid of its area!
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So, the two sides of the triangle have the same result and considered a new base with corresponding new altitude. The centroid lies at the intersection of the median. Since, the distance of this point from any side is one-third, the altitude of the triangle with that side considered the base.
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VOLUME
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THEOREMS OF PAPPUS
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BEAMS—EXTERNAL EFFECTS
• Beams are structural members which offer resistance to bendingdue to applied loads.
• Most beams are long prismatic bars, and the loadsare usually applied normal to the axes of the bars.
Types of Beam
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DISTRIBUTED LOADS
The Formula
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BEAMS—INTERNAL EFFECTSShear, Bending, and Torsion• The force V is called the shear
force
• the couple M is called thebending moment
• the couple T is called a torsional moment.
• These effects represent the vector components of the resultant of the forces acting on a transverse section of the beam as shown in the lower part of the figure.
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CABLE
Flexible Cable Parabolic Cable
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Catenary Cable