Beam Analysis
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Transcript of Beam Analysis
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Beam Analysis
We require from buildings two kinds of goodness: first, the doing their practical duty well: then that they be graceful and pleasing
in doing it. -John Ruskin
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Beam
• Structural member that carries a load that is applied transverse to its length
• Used in floors and roofs
• May be called floor joists, stringers, floor beams, or girders
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• The loads are initially applied to a building surface (floor or roof).
• Loads are transferred to beams which transfer the load to another building component.
Gird
er
Beam Gird
er
Beam
Chasing the Load
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Static Equilibrium
• The state of an object in which the forces counteract each other so that the object remains stationary
• A beam must be in static equilibrium to successfully carry loads
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Static Equilibrium
• The loads applied to the beam (from the roof or floor) must be resisted by forces from the beam supports.
• The resisting forces are called reaction forces.
Applied Load
Reaction Force
Reaction Force
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Reaction Forces
• Reaction forces can be linear or rotational.– A linear reaction is often called a shear reaction (F or R).– A rotational reaction is often called a moment reaction
(M).
• The reaction forces must balance the applied forces.
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Beam Supports
The method of support dictates the types of reaction forces from the supporting members.
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Beam Types
Simple
Continuous
Cantilever Moment
(fixed at one end)
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Beam Types
Fixed
Moments at each end
Propped – Fixed at one end; supported at other
Overhang
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Simple Beams
Applied Load
BEAM DIAGRAM
FREE BODY DIAGRAM
Applied Load
Note: When there is no applied horizontal load, you may ignore the horizontal reaction at the pinned connection.
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Fundamental Principles of Equilibrium
Fy = 0 The sum of all vertical forces acting on a body must equal
zero.
Fx = 0 The sum of all horizontal forces acting on a body must
equal zero.
Mp = 0 The sum of all moments (about any point) acting on a
body must equal zero.
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Moment
• A moment is created when a force tends to rotate an object.
• The magnitude of the moment is equal to the force times the perpendicular distance to the force (moment arm).
F
M
M dF d moment arm
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Calculating Reaction Forces
Sketch a beam diagram.
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Calculating Reaction Forces
Sketch a free body diagram.
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Calculating Reaction Forces
Use the equilibrium equations to find the magnitude of the reaction forces.– Horizontal Forces– Assume to the right is positive
+
xF 0
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Calculating Reaction Forces
• Vertical Forces
• Assume up is positive +
Equivalent Concentrated Load
Equivalent Concentrated Load
yF 0
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Calculating Reaction Forces
• Moments• Assume counter clockwise rotation is positive
+
A B
0 == 7700 lb
20 4000 6 13 000 10 0 0 yB yA( F ft ) ( lb ft ) ( , lb ft ) ( F )
20 24 000 130 000 0 0 yB( ft )F , ft lb , ft lb
20 154 000 yB( ft )F , ft lb
154 000
20
yB
, ft lbF
ft
7 700yBF , lb
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Calculating Reaction Forces
• Now that we know , we can use the previous equation to find .
= 7700 lb9300 lb =
0 =
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Shear Diagram
= 7700 lb9300 lb =
0 =
Shear at a point along the beam is equal to the reactions (upward) minus the applied loads (downward) to the left of that point.
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Moment Diagram
1400215
650
lbft
lbx . ft
Kink in moment curve
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Moment Diagram
9300 lb =
0 =
4000 lb
2.15’
MP
. ftlbft( lb )( . ft ) ( )(M . ft ) ( ) ( lb )( . ft )815
24000 215 650 815 9300 815 0
45608 maxMM ft lb
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Moment Diagram
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Moment Diagram
A
B
C
= 2.15 ft
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Beam Analysis
• Example : simple beam with a uniform load, w1= 1090 lb/ft
• Span = 18 feet
Test your understanding: Draw the shear and moment diagrams for this beam and loading condition.
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Moment
Shear
Max. Moment = 44,145l ft-lb Max. Shear = 9,810 lb
Shear and Moment Diagrams