Design of Columns and Beam-Columns in Timber

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Design of Columns and Beam-Columns in Timber - PowerPoint PPT Presentation

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. L eff. Δ. P. Truss compression members Fraser Bridge, Quesnel. Column behaviour.

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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

Leff

Δ

P

Truss compression members

Fraser Bridge, Quesnel

Column behaviour

Perfectly straight and elastic column

Pcr

P

Crooked elastic column

Leff

Δ

Axial load P (kN)

Crooked column with material failure

P

Displacement Δ (mm)

Pin-ended struts

Burnaby

Column design equation

P

axis of buckling

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

Glulam arches and cross-bracing

UNBC, Prince George, BC

material failure

Capacity of a column

FcA

Pr

combination of material failure and buckling

π2EI/L2 (Euler equation)

elastic buckling

Le

Pin-ended columns in

restroom building

North Cascades Highway, WA

Non-prismatic round columns

Actual pin connections

Column buckling factor KC

1.0

KC

limit

 0.15

CC = Le/d

50

What is an acceptable l/d ratio ??

Clustered columns

Forest Sciences Centre, UBC

L/d ration of individual columns ~ 30

P

P

P

P

P

P

P

P

P

P

Effective lengthLeff = length of half sine-wave = k L

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 base

Note: water damage

Le

Ley

Lex

L/d ratios

y

y

x

x

y

y

d

dx

dy

Stud wall

axis of buckling

d

L

ignore sheathing contribution when calculating stud wall resistance

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)

P

P

P

P

P

P

P

P

P

P

Le

Le

Le

Le

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

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)

Htotal = H

 = amplification factor

H = applied hor. load

W

H

Δ

h

Δ = 1st order displacement

Haunched frame in longitudinal direction

Sway frame for a small covered road bridge

Combined stresses

Bi-axial bending

Bending and compression

Heavy timber trusses

Abbotsford arena

Pf

fa = Pf / A

neutral axis

x

fbx = Mfx / Sx

Mfx

x

y

fby = Mfy / Sy

Mfy

y

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

The only fly in the pie is that fdes is not the same for the three cases

Moment amplification

P

Δo

Δmax

PE = Euler load

P

Interaction equation

wall and top plate help to distribute loads into studs

joists

top plate

wall plate

d

L

studs

sill plate

check compression perp.