ENGR 220 Section 13'113'2 - PowerPoint PPT Presentation

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ENGR 220 Section 13'113'2

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Circular tubes, Square tubes. Better than. Solid sections. Critical Stress ... the bottom and is braced at the top by cables to prevent movement along X axis. ... – PowerPoint PPT presentation

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Title: ENGR 220 Section 13'113'2

1
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
centroidLinearly elasticColumn bends in a
single plane
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Relate v to Moment via Deflection Equation
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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.
a-a not
b-b
Circular tubes, Square tubes Better than Solid
sections.
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Critical Stress
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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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