Post on 15-Dec-2015
Axial Force Member Design
CE A433 – Spring 2008T. Bart Quimby, P.E., Ph.D.
University of Alaska AnchorageCivil Engineering
Tension Members
• Members subject to axial tension include truss elements, diaphragm chords, and drag struts.
• The basic Design Inequality is:
ASD: ft < F’tTa/An < Ft CDCMCF
LRFD: Tu < T’nTu < KFFt CMCF 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’cPa/A < Fc CDCMCFCP
LRFD: Pu < P’nPu < KFFt CMCFCP 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 plane of buckling
• Most members have two principle directions and lu is frequently different in each direction.
Weak Axis Buckling
Strong Axis Buckling
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 CoefficientsFrom 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 Axial Force and Bending
• Both axial force and bending create normal stresses on a cross section.
total, x,y = axial + bending-x + bending-y
x,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.
axial < axial,allowable
bending-x < bending-x,allowable
bending-y < bending-y,allowable
combined < combined,allowable
Combining Allowable Stress
• These can be rewritten as the following ratios:
axial / axial,allowable < 1.00bending-x / bending-x,allowable < 1.00bending-y / bending-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
axial / a,allow + bx / bx,allow + by / by,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