Design of Columns and
Beam-Columns in Timber
Column failures
• Material failure (crushing)
• Elastic buckling (Euler)
• Inelastic buckling (combination of
buckling and material failure)
P
P
ΔLeff
Truss compression members
Fraser Bridge, Quesnel
Column behaviour
Displacement Δ (mm)
Axi
al l
oad
P (
kN)
Pcr
P
P
Δ
Perfectly straight and elastic column
Crooked elastic column
Crooked column with material failure
2
2
effcr L
EIP
Leff
Pin-ended struts
Shadbolt Centre, Burnaby
Column design equation
Pr = Fc A KZc KC
where = 0.8
and Fc = fc (KD KH KSc KT)
size factor KZc = 6.3 (dL)-0.13 ≤ 1.3
d
L
axis of bucklingP
Glulam arches and cross-bracing
UNBC, Prince George, BC
Capacity of a column
Le
Pr
combination of material failure and buckling
elastic buckling
material failure
FcA
π2EI/L2 (Euler equation)
Pin-ended columns in restroom building
North Cascades Highway, WA
Actual pin connections
Non-prismatic round columns
Column buckling factor KC
CC = Le/d
KC
1.0
1
05
3
350.1
TSE
CZccC KKE
CKFK
50
limit
0.15
What is an acceptable l/d ratio ??
Clustered columns
Forest Sciences Centre, UBC
L/d ration of individual columns ~ 30
Effective lengthLeff = length of half sine-wave = k L
k (theory) 1.0 0.5 0.7 > 1
k (design) 1.0 0.65 0.8 > 1
non-sway non-sway non-sway sway*
P PP P P
P P PPP
Le Le Le Le
* Sway cases should be treated with frame stability approach
Glulam and steel trusses
Velodrome, Bordeaux, France
All end connections are assumed to be pin-ended
Pin connected column baseNote: water damage
Column base: fixed or pin connected ??
Effective length
Lex
Ley
Round poles in a marine structure
Partially braced columns in a post-and-beam structure
FERIC Building, Vancouver, BC
L/d ratios
Le
Ley
Lex
d
dy
dx
x
x
y
y
y
y
Stud wallaxis of buckling
d
Lignore sheathing contribution when calculating stud wall resistance
Stud wall construction
Fixed or pinned connection ?
Note: bearing block from hard wood
An interesting connection between column and truss
(combined steel and glulam truss)
Slightly over-designed truss member
(Architectural features)
Effective length (sway cases)Leff = length of half sine-wave = k L
k (theory) 1.0 2.0 2.0 1.0<k<2.0
k (design) 1.2 2.0 2.0 1.5
P PP P P
P P PPP
Note: Sway cases should only be designed this way when all the columns are equally loaded and all columns contribute equally to the lateral sway resistance of a building
Le
Le
Le
Le
Sway frame for a small covered road bridge
Sway permitted columns….or aren’t they ??
Haunched columns
UNBC, Prince George, BC
Frame stability
• Columns carry axial forces from gravity loads• Effective length based on sway-prevented case• Sway effects included in applied moments
– When no applied moments, assume frame to be out-of-plumb by 0.5% drift
– Applied horizontal forces (wind, earthquake) get amplified
• Design as beam-column
Frame stability(P- Δ effects)
Δ
HW
Δ = 1st order displacement
Htotal = H = amplification factorH = applied hor. load
h
HhW
1
1
Note: This column does not contribute to the stability of the frame
Sway frame for a small covered road bridge
Haunched frame in longitudinal direction
Minimal bracing, combined with roof diaphragm in lateral direction
Combined stresses
Bi-axial bending
Bending and compression
Heavy timber trusses
Abbotsford arena
Roundhouse Lodge, Whistler Mountain
neutral axis
fmax = fa + fbx + fby < fdes
( Pf / A ) + ( Mfx / Sx ) + ( Mfy / Sy ) < fdes
(Pf / Afdes) + (Mfx / Sxfdes) + (Mfy / Syfdes) < 1.0
(Pf / Pr) + (Mfx / Mr) + ( Mfy / Mr) < 1.0
x
x
fbx = Mfx / Sx
Mfx
y
yfby = Mfy / Sy Mfy
The only fly in the pie is that fdes is not the same for the three cases
fa = Pf / A
Pf
Moment amplification
Δo Δmax
P
P
0max
0max
1
1
1
1
MPP
M
PP
E
E
PE = Euler load
Interaction equation
0.11
1
1
1
ry
fy
Eyrx
fx
Exr
f
M
M
PPM
M
PPP
P
Axial load
Bending about y-axis
Bending about x-axis
3 storey walk-up (woodframe construction)
New Forestry Building, UBC, Vancouver
Stud wall construction
sill plate
d
L
studs
top platewall plate
joists
check compression perp.
wall and top plate help to distribute loads into studs