Lecture 31 Biaxial Column

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Lecture 31 - Biaxial Column

• November 13, 2002
• CVEN 444

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Lecture Goals

• Short Column Biaxial Design

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Biaxial Column Example
The section of a short tied column is 16 x 24 in.
and is reinforced with 8 10 bars as shown.
Determine the allowable ultimate load on the
section f Pn if its acts at ex 8 in. and ey
12 in. Use fc 5 ksi and fy 60 ksi.
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Biaxial Column Example
Compute the P0 load, compression with no moments
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Biaxial Column Example
Compute Pnx, by starting with ey term and assume
that compression controls. Check by Compute
the nominal load, Pnx and assume second
compression steel does not contribute
assume small
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Biaxial Column Example
The components of the equilibrium equation
are Use similar triangles to find the
stress in the steel, fs
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Biaxial Column Example
Compute the moment about the tension
steel where The resulting equation is
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Biaxial Column Example
Combine the two equations and solve for Pn using
an iterative solution Set the two equation
equal to one another and sole for fs and the
definition
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Biaxial Column Example
Combine the two equations and solve for c using
an iterative technique You are solving a cubic
equation
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Biaxial Column Example
Check the assumption that Cs2 is close to zero
This value is small relative to the others
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Biaxial Column Example
This Cs2 11 kips relatively small verses the
overall load, which is So Pnx 733.0 kips
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Biaxial Column Example
Start with ex term and assume that compression
controls. Compute the nominal load, Pny and
assume second compression steel does not
contribute
assume small
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Biaxial Column Example
The components of the equilibrium equation are
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Biaxial Column Example
Compute the moment about the tension
steel where The resulting equation is
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Biaxial Column Example
Combine the two equations and solve for Pn using
an iterative solution Set the two equation
equal to one another and sole for fs and the
definition
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Biaxial Column Example
Combine the two equations and solve for c using
an iterative technique You are solving a cubic
equation
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Biaxial Column Example
Check the assumption that Cs2 is close to zero
This value is negative so it does not contribute
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Biaxial Column Example
This Cs2 - 2.1 kips relatively small verses the
overall load, which is So Pnx 684.6 kips
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Biaxial Column Example
Compute the nominal load
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Biaxial Column Example
Note the Pnx Pny include the corner steel bars
in both calculations a more conservative solution
would be to use 1/2 the steel in each direction
so As 2(1.27 in2) which would reduce Pu .
(Remember fs can not be greater than 60 ksi, so
that Pnx 620.3 k and Pny 578.4 k Pn 360.7
k and Pu 234.5 k )
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Homework due (11/25/02)