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ARCH5023/ARCH4333 - ARCHITECTURAL STRUCTURES I

][ STEEL STRUCTURES ][
THE UNIVERSITY OF OKLAHOMA - COLLEGE OF ARCHITECTURE
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STEEL COLUMNS

WITH BENDING

COLUMNS WITH BENDING
======================
PA 330

Bending in addition to axial compression
=============================
	a. eccentricity
			due to supports on column face
			brackets etc.
	b. moment-resistive connection
			rigid frame 
	c. wind = beam load
	d. horizontal load
			from cars
			earth quakes
			explosions

Theory:
======
	buckling effect of column
	combined with
	effects of laterally unsupported beam
	P-delta effect
		PA 230

P-Delta Effect:
===========
(PA 230)
Occurs when the deflection
due to bending
moves the centroid of the column at midheight
away from the line of action 
of the axial compression force.
This results in some additional bending moment
of a magnitude equal to the product of
compression force (P)
times the deflection (delta)
The entire moment is a P-delta effect.


			Equivalent Design Load
			=================
		      that incorporates the bending effect
		      =========================
	
			P' = P + BxMx + ByMy

P' 	= equivalent axial load
P 	= actual axial load
Bx 	= bending factor for the section's x-axis
Mx	= bending moment about the x-axis	
By 	= bending factor for the section's y-axis	
My	= bending moment about the y-axis.
Bx & By Table 10.2 PA 321 & 322
Equivalent Design Load
that incorporates the bending effect

EXAMPLE PROBLEM

Equivalent Design Load that incorporates the bending effect

Example Problem: 
=============
Equivalent Design Load that incorporates the bending effect
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
It is desired to use a 10 in W shape
for a column that sustains an
axial compression plus bending.
The axial compression load from above
is 120 kips
and the beam load is 24 kips
with the beam attached at the column face.
The Column is 16 ft high and
has a K factor of 1
Select a trial section for the column

A. GIVEN

10 inch W shaped column
axial compression load from above = 120 kips
beam load = 24 kips
beam attached at the column face.
column height = 16 ft 
K factor = 1

B. ASKED

Select a trial section for the column.

C. DIAGRAM


			| Pc = 120 kips
			|
			|	| Pb = 24 kips
			===
			|	|
			|	|_________
			|	|_________
			|	|
			|	|
			===

			|----|
			  10"

D. SOLUTION

1. Bending occurs only about the x-axis
	only Bx factor is critical

2. Table 10.2 PA 321 
	scanning the column of Bx factors
	observe that factor for 10 W sections
	range from 0.261  -  0.2777

3. We have not yet determined the section to be used.
	It is necessary to make an assumption
	for the factor and verify the assumption
	after the selection is made.
	Let us assume a Bx of 0.27 

4. 		P' = P + BxMx + ByMy

P' 	= equivalent axial load
P 	= actual axial load
Bx 	= bending factor for the section's x-axis
Mx	= bending moment about the x-axis	
By 	= bending factor for the section's y-axis	
My	= bending moment about the y-axis.

5.
P = P c + P b
P = 120 kips + 24 kips
P = 144 kips
P c = load from column 
P b = load from beam	 

6. Bending occurs only around the x-axis
    By = 0
    My = 0

7. P' = P + BxMx + ByMy
	   = 144 kips + 0.27  (Pb x d/2)
	       Pc + Pb + table           10"/2	 
P' = (120 + 24 kips) + 0.27 (24 kips) x (5in) 
P' = 144 + 32.4
P' = 176.4 kips

8. K L
    K = 1   given
    L = 16 ft
    K L
    1 x 16
    K L = 16

9. Table 10.2 PA 321
	KL = 16
	P' = 144 kips
	W 10 given

10. W 10 X 45 SELECTED

11. Bx = 0.271
      very close to our assumption of 0.27

E. ANSWER









STEEL COLUMNS RELATED SITES




W Shapes




M Shapes




Pipe Columns




Tubular Columns




Double-Angle Compression Members




Cold Formed C





 
 














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Dr. Hermann Gruenwald




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©Dr. Gruenwald 1996, 1997