ENGR 220 Section 13'113'2

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ENGR 220Section 13.113.2
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Buckling of Columns
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Column Buckling
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Ideal Column
BucklingIdeal Column Pin supports at both
endsHomogenous materialLoad applied through
centroidLinearly elasticColumn bends in a
single plane
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Relate v to Moment via Deflection Equation
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Maximum Axial Load Euler Load
Deflected shape is a sine curve
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Column Length

• Shorter is better
• If you double the length then the maximum axial
  load decreases by a factor of four.

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Modulus of Elasticity

• Maximum axial load is independent of the yield
  strength of the material.
• High strength steel is no advantage over low
  strength steel.

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Moment of Inertia

• I ? y2 dA
• Second moment of Area
• The load carrying capability of a column
  increases as the moment of inertia of a column
  increases.
• Columns will buckle about the principal axis
  having the least moment of inertia.

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Efficient Columns have cross sectional area
located as far as possible from centroidal axes.
This column buckles about
a-a not
b-b
Circular tubes, Square tubes Better than Solid
sections.
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Critical Stress
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Radius of Gyration
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Types of Supports

• Pinned Pinned (Euler Column)
• Fixed Free
• Fixed Fixed
• Fixed Pinned

Moment equation and Boundary Conditions
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Effective Length Le K L Effective Length
Slenderness Ratio Le/r
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The Al column is fixed at the bottom and is
braced at the top by cables to prevent movement
along X axis. Determine the largest allowable P
that can be applied. F.S. 3, EAl 70 GPa,
yield stress 215 MPa, A 7.5 x 10-3 m2, Ix
61.3 x 10-6 m4, Iy 23.2 x 10-6 m4
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13.2 The column consists of a Rigid member
pinned at the bottom and attached to a spring at
the top. When the column is in vertical position,
the spring is unstretched. Determine the critical
load P that can be placed on the column.
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13.22 Member BD in the truss below, is an A-36
steel rod of radius 2 inches. Determine maximum
load that can be supported by the truss without
causing member BD to buckle. All members are pin
connected.
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13. 31 The linkage is made using two A-36 steel
rods, each having a circular cross section.
Determine the diameter of each rod to the nearest
1/8th in. that will support the 900 lb load
without buckling. Factor of Safety 1.8.
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13.42 The 50 mm diameter C86100 Bronze rod is
fixed at A and has a gap of 2 mm from the wall at
B. Determine the increase in temperature that
will cause rod AB to buckle. Contact at B acts as
a pin.