Design of Columns and BeamColumns in Timber Column

Design of Columns and Beam-Columns in Timber

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

Truss compression members Fraser Bridge, Quesnel

Column behaviour Perfectly straight and elastic column Pcr P Axial load P (k. N) Crooked elastic column Leff Δ Crooked column with material failure P Displacement Δ (mm)

Pin-ended struts Shadbolt Centre, 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 (d. L)-0. 13 ≤ 1. 3 d L

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

Capacity of a column Fc A Pr material failure combination of material failure and buckling π2 EI/L 2 (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

Effective length Leff = length of half sine-wave = k L P Le P P P Le Le P P P k (theory) 1. 0 0. 5 0. 7 >1 k (design) 1. 0 0. 65 0. 8 >1 non-sway sway* * 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 Ley Lex

Round poles in a marine structure

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

L/d ratios y y x x y y Ley d Le Lex dy dx

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) Leff = length of half sine-wave = k L P P P Le Le P P P k (theory) 1. 0 2. 0 1. 0<k<2. 0 k (design) 1. 2 2. 0 1. 5 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 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 outof-plumb by 0. 5% drift – Applied horizontal forces (wind, earthquake) get amplified • Design as beam-column

Frame stability Htotal = H = amplification factor H = applied hor. load (P- Δ effects) W H Δ h Δ = 1 st order displacement Note: This column does not contribute to the stability of the frame

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

Bi-axial bending Bending and compression Combined stresses

Heavy timber trusses Abbotsford arena

Roundhouse Lodge, Whistler Mountain

Pf fa = P f / A neutral axis x fbx = Mfx / Sx fmax = fa + fbx + fby < fdes Mfx ( Pf / A ) + ( Mfx / Sx ) + ( Mfy / Sy ) < fdes x (Pf / Afdes) + (Mfx / Sxfdes) + (Mfy / Syfdes) < 1. 0 fby = Mfy / Sy y Mfy y (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