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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
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.

18
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
25
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
26
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.
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