Transcript Design of Timber Bending Members

Design of Combined Bending and
Compression Members in Steel
Bi-axial bending
Bending and
compression
Combined stresses
Multi-story steel
rigid frame
•
Rigid frames, utilizing moment connections, are well suited for specific types
of buildings where diagonal bracing is not feasible or does not fit the
architectural design
•
Rigid frames generally cost more than braced frames
(AISC 2002)
Vierendeel steel truss cycle bridge
Beaufort Reach, Swansea
Typical crane columns
Pf
fa = Pf / A
neutral axis
x
fmax = fa + fbx + fby < fdes
fbx = Mfx / Sx
Mfx
( Pf / A ) + ( Mfx / Sx ) + ( Mfy / Sy ) < fdes
x
(Pf / Afdes) + (Mfx / Sxfdes) + (Mfy / Syfdes) < 1.0
fby = Mfy / Sy
y
y
Mfy
(Pf / Pr) + (Mfx / Mr) + ( Mfy / Mr) < 1.0
Cross-sectional strength
Pf/Pr
1.0
Class 1 steel sections
(Pf / Pr) + 0.85(Mfx / Mr) + 0.6( Mfy / Mr) < 1.0
other steel sections
(Pf / Pr) + (Mfx / Mr) + ( Mfy / Mr) < 1.0
1.0
Mf/Mr
Slender beam-columns
• What if column buckling can occur ?
• What if lateral-torsional buckling under
bending can occur ?
Use the appropriate axial resistance
and moment resistance values in the
interaction equation
Beam-column in
a heavy
industrial setting
BMD
Moment amplification
P
 max
δo


1
 0
 
 1  P PE 
δmax
M max
P


1
 M 0
 
 1  P PE 
PE = Euler load
Interaction equation
 1x  M fx  1 y  M fy


 

 1.0
Pr  1  P PEx  M rx  1  P PEy  M ry
Pf
Axial
load
Bending
about x-axis
Bending
about y-axis
ω1 = moment gradient factor (see next slide)
M1
Moment gradient factor
for steel columns with
end moments
ω1 = 0.6 – 0.4(M1/M2) ≥ 0.4
i.e. when moments are
equal and cause a single
curvature, then ω1 = 1.0
M2
and when they are equal
and cause an s-shape, then
ω1 = 0.4
Steel frame to resist
earthquake forces
Warehouse building, Los Angeles
Moment gradient factor for other cases
v
ω1 = 1.0
ω1 = 1.0
ω1 = 0.85
ω1 = 0.6
ω1 = 0.4
Design of steel beam-columns
1. Laterally supported
•
Cross-sectional strength
2. Supported in the y-direction
•
•
•
Overall member strength
Use moment amplification factor
Use buckling strength about x-axis (Crx)
3. Laterally unsupported
•
•
•
•
Buckling about y-axis (Cry)
Lateral torsional buckling (Mrx)
Use moment amplification factors
Usually the most critical condition
Note: Mry never includes lateral-torsional buckling
Example of different support conditions
This column unsupported
These two columns
supported in y-direction
by side wall
x direction
y direction