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 Δ L eff

Truss compression members Fraser Bridge, Quesnel

Column behaviour Displacement Δ (mm) Axial load P (kN) P cr P P Δ Perfectly straight and elastic column Crooked elastic column Crooked column with material failure L eff

Pin-ended struts Shadbolt Centre, Burnaby

Column design equation P r =  F c A K Zc K C where  = 0.8 and F c = f c (K D K H K Sc K T ) size factor K Zc = 6.3 (dL) ≤ 1.3 d L axis of buckling P

Glulam arches and cross-bracing UNBC, Prince George, BC

Capacity of a column LeLe PrPr combination of material failure and buckling elastic buckling material failure  FcA FcA π 2 EI/L 2 (Euler equation)

Pin-ended columns in restroom building North Cascades Highway, WA Actual pin connections Non-prismatic round columns

Column buckling factor K C C C = L e /d KCKC limit  0.15

What is an acceptable l/d ratio ?? Clustered columns Forest Sciences Centre, UBC L/d ration of individual columns ~ 30

Effective length L eff = length of half sine-wave = k L k (theory) > 1 k (design) > 1 non-sway sway* P PP PP P PPPP LeLe LeLe LeLe LeLe * 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

Column base: fixed or pin connected ??

Effective length L ex L ey

Round poles in a marine structure

Partially braced columns in a post- and-beam structure FERIC Building, Vancouver, BC

L/d ratios LeLe L ey L ex d dydy dxdx x x y y y y

Stud wall axis of buckling d L ignore 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) L eff = length of half sine-wave = k L k (theory) <k<2.0 k (design) P PP PP P PPPP 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 LeLe LeLe LeLe LeLe

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 H W Δ = 1 st order displacement H total =  H  = amplification factor H = applied hor. load h 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 f max = f a + f bx + f by < f des ( P f / A ) + ( M fx / S x ) + ( M fy / S y ) < f des (P f / A f des ) + (M fx / S x f des ) + (M fy / S y f des ) < 1.0 (P f / P r ) + (M fx / M r ) + ( M fy / M r ) < 1.0 x x f bx = M fx / S x M fx y y f by = M fy / S y M fy The only fly in the pie is that f des is not the same for the three cases f a = P f / A PfPf

Moment amplification ΔoΔo Δ max P P P E = Euler load

Interaction equation 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 plate wall plate joists check compression perp. wall and top plate help to distribute loads into studs