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Design of Columns and Beam-Columns in Timber

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Column failures Material failure (crushing) Elastic buckling (Euler) Inelastic buckling (combination of buckling and material failure) P P Δ L eff

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Truss compression members Fraser Bridge, Quesnel

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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

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Pin-ended struts Shadbolt Centre, Burnaby

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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) -0.13 ≤ 1.3 d L axis of buckling P

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

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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)

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

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Column buckling factor K C C C = L e /d KCKC 1.0 50 limit 0.15

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

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Effective length L eff = length of half sine-wave = k L k (theory)1.00.50.7> 1 k (design)1.00.650.8> 1 non-sway sway* P PP PP P PPPP LeLe LeLe LeLe LeLe * Sway cases should be treated with frame stability approach

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Glulam and steel trusses Velodrome, Bordeaux, France All end connections are assumed to be pin-ended

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Pin connected column base Note: water damage

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Column base: fixed or pin connected ??

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Effective length L ex L ey

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Round poles in a marine structure

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

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

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Stud wall axis of buckling d L ignore sheathing contribution when calculating stud wall resistance

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Stud wall construction

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Fixed or pinned connection ? Note: bearing block from hard wood

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An interesting connection between column and truss (combined steel and glulam truss)

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Slightly over-designed truss member (Architectural features)

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Effective length (sway cases) L eff = length of half sine-wave = k L k (theory)1.02.0 1.0

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Sway frame for a small covered road bridge

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Sway permitted columns ….or aren’t they ??

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Haunched columns UNBC, Prince George, BC

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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

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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

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Sway frame for a small covered road bridge Haunched frame in longitudinal direction Minimal bracing, combined with roof diaphragm in lateral direction

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Combined stresses Bi-axial bending Bending and compression

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Heavy timber trusses Abbotsford arena

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Roundhouse Lodge, Whistler Mountain

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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

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

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Interaction equation Axial load Bending about y-axis Bending about x-axis

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3 storey walk-up (woodframe construction)

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New Forestry Building, UBC, Vancouver

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Stud wall construction

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sill plate d L studs top plate wall plate joists check compression perp. wall and top plate help to distribute loads into studs

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