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