Axial Force Member Design
CE A433 – Spring 2008
T. Bart Quimby, P.E., Ph.D.
University of Alaska Anchorage
Civil Engineering
Tension Members
• Members subject to axial tension include
truss elements, diaphragm chords, and
drag struts.
• The basic Design Inequality is:
ASD: ft < F’t
Ta/An < Ft CDCMCF
LRFD: Tu < fT’n
Tu < f KFFt lCMCF An
An: Net Area
• Net Area accounts for
loss of area due to
holes and other cuts
in the member.
• Net Area is the gross
area less the area of
any grain that is cut.
• There is no account
for stagger.
Compression Members
• Members subject to axial compression
include columns, studs, truss elements,
diaphragm chords, and drag struts.
• The basic Design Inequality is:
ASD: fc < F’c
Pa/A < Fc CDCMCFCP
LRFD: Pu < fP’n
Pu < f KFFt lCMCFCP A
A: Area
• In Buckling Region
– A = Gross Area, Ag
• In Non-Buckling Regions
(i.e. near ends in most
cases)
– A = Net Area, An
CP: Column Stability Factor
• Applies only to
compressive stress, Fc
• Applies to both Sawn
Lumber and Glulams
• Found in NDS 3.7.1
– This factor accounts for
instability in laterally
unsupported columns
(i.e. column buckling)
– Different in each principle
direction
More CP
• See NDS Equation 3.7-1
• Column buckling is a function of the laterally unbraced
(buckling) length, le, and cross section properties
(Moment of Inertia, Ie, and Area, A) and is different in
each principle cross section direction.
• First check the slenderness ratio
– le/d must not exceed 50
• Then compute CP
• Note that CP is a function of the member size!
– This means that you must know the member size before
computing this factor
– When designing, this dependency leads to iterative
computations
Laterally Unbraced Length, lu
• This is the distance
between locations of
lateral support in the
Weak Axis
plane of buckling
Buckling
• Most members have
Strong Axis
two principle
Buckling
directions and lu is
frequently different in
each direction.
le: Effective Length
• Effective length is
a function of the
laterally unbraced
length and the
end conditions.
• Most timber
connections are
considered to be
pinned.
Effective Length Coefficients
From AISC Steel Construction Manual
Slenderness
• NDS 3.7.1.4
• The slenderness ratio le/d
must not exceed 50
– luy1/d1, luy2/d1
– lux1/d2
Computing CP
• NDS Equation 3.7-1
• Accounts for buckling and material
strengths
Material Strength
Euler Strength
Combined Bending & Axial
Force
NDS 3.9
Combined Axial Force and
Bending
• Both axial force and bending create normal
stresses on a cross section.
stotal, x,y = saxial + sbending-x + sbending-y
sx,y = P/A + Mxy/Ix + Myx/Iy
• The result is a planar equation across the
section.
Allowable Composite Stress
• Note that each stress component has a
DIFFERENT allowable stress, so the limiting
value of the combined stress needs to be a
composite of the individual allowable stresses.
saxial < saxial,allowable
sbending-x < sbending-x,allowable
sbending-y < sbending-y,allowable
scombined < scombined,allowable
Combining Allowable Stress
• These can be rewritten as the following ratios:
saxial / saxial,allowable < 1.00
sbending-x / sbending-x,allowable < 1.00
sbending-y / sbending-y,allowable < 1.00
• In each case, the ratio goes to 1.0 as the normal
stress approaches it’s allowable
Interaction Equation
• Instead of finding a composite allowable
stress, we can combine the stress ratios
saxial / sa,allow + sbx / sbx,allow + sby / sby,allow < 1.00
• Most combined stress and combined force
equations used in structural engineering
use this form.
Second Order Effects
• Secondary moments are created with axial force
is applied to an already bent member.
• See text in A Beginner’s Guide to the Steel
Construction Manual, section 10.3 for more
explanation about second order effects.
• Second order effects are ignored in combined
tension and bending
• Second order effects can be very significant in
combined compression and bending
Bending & Axial Tension
• NDS 3.9.1
• Both interaction equations must be
satisfied.
Bending & Axial Compression
• NDS 3.9.2
• Moments are
“magnified” by the
factors
M1
1  f c

FcE1 

M2
2
 fc

f b1


1  F   F  
cE 2
bE 


