design of timber columns and beam-columns
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8/9/2019 Design of Timber Columns and Beam-Columns
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Design of
Beam-Columnsin Timber
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• a er a a ure crus ng•
• Inelastic bucklin combination of
buckling and material failure) ∆Leff
P
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2 EI
P
π
= eff
cr L
Pcr P
er ec y s ra g an e as c co umn
Crooked elastic column
( k N
)
a l l o a d P
∆
Crooked column with material failure
Leff
A x
Displacement ∆ (mm)
P
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Shadbolt Centre,
Burnaby
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axis of
bucklingP
Pr = Fc A KZc KC
where = 0.8d
and Fc = f c (KD KH KSc KT)
size factor K = 6.3 dL -0.13 ≤ 1.3
L
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Glulam arches and
cross-bracing
UNBC, Prince George, BC
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Ca acit of a column
material failure
FcA
r
combination of
material failure and
buckling
π u er equa on
elastic buckling
Le
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1
3 −
1.0
05350.1 ⎥⎢ += T SE
C ZccC
K K E K
KC
limit
± 0.15
CC = Le /d50
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What is an acceptable
ra o
Clustered columns
Forest Sciences Centre, UBC
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Effective lengthLeff = length of half sine-wave = k L
P PP P P
e e e e
k theor 1.0 0.5 0.7 > 1
P P PPP
k (design) 1.0 0.65 0.8 > 1
non-sway non-sway non-sway sway*
* 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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length
Lex
Ley
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Round poles in a marine structure
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Partiall braced
columns in a post-and-beam structure
u ng,
Vancouver, BC
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L/d ratiosx
yy
x
yy
L
ey
Lex
d
dd
x
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buckling
d
Lgnore s ea ng
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)Leff = length of half sine-wave = k L
P PP P P
Le
Le
Le
Le
k theor 1.0 2.0 2.0 1.0
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Sway frame for a
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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•
• Effective length based on sway-prevented case•
– When no applied moments, assume frame to be out-
of-plumb by 0.5% drift – Applied horizontal forces (wind, earthquake) get
amplified
• es gn as eam-co umn
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Frame stability(P- ∆ effects)Htotal = H
= amplification factor
H
W .
∆
h
W Δ−
=1
α
Note: This column does
∆ = 1st order displacement
not contribute to the
stability of the frame
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Sway frame for a
bridge
Minimal bracing,combined with roof
diaphragm in lateral
Haunched frame in
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Bi-axial bending
Bending and
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Heavy timber trusses
Abbotsford arena
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Roundhouse Lodge, Whistler Mountain
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Pf a = Pf / A
neu ra ax s
xmax a bx by des
( Pf / A ) + ( Mfx / Sx ) + ( Mfy / Sy ) < f des
f bx = Mfx / SxMfx
(Pf / Af des) + (Mfx / Sxf des) + (Mfy / Syf des) < 1.0
x
(Pf / Pr ) + (Mfx / Mr ) + ( Mfy / Mr ) < 1.0by fy y
Mfy
ye on y y n e p e s a des s
not the same for the three cases
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P
0max1 Δ⎟⎜⎛ =Δ
∆o
∆max
E −
0max
1 PP E ⎟⎜
⎝ −=
=
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0.111 ≤⎟⎟⎜⎜ −+⎟⎟⎜⎜ −+ r
fy
E rx
fx
Exr
f
M PP M PPP
Axial BendinBendinload about y-axisabout 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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wall and top plate
o s s loads into studs
d
op p a e
wall plate
L
studs
check
compression perp.
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