Transcript Design of Timber Bending Members

Design of
Columns and
Beam-Columns
in Timber
Column failures
• Material failure (crushing)
• Elastic buckling (Euler)
P
• Inelastic buckling (combination of
buckling and material failure)
Leff
Δ
P
Truss compression members
Fraser Bridge, Quesnel
Pcr 
 EI
2
2
eff
L
Column behaviour
Perfectly straight and elastic column
Pcr
P
Axial load P (kN)
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 (dL)-0.13 ≤ 1.3
d
L
Glulam arches and
cross-bracing
UNBC, Prince George, BC
Capacity of a column
 FcA
Pr
material failure
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

Fc K Zc C 
K C  1.0 

35E05 K SE KT 

3
C
1.0
KC
limit
 0.15
CC = Le/d
50
1
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
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
non-sway
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
P
P
Le
Le
Le
Le
P
P
P
P
P
k (theory)
1.0
2.0
2.0
1.0<k<2.0
k (design)
1.2
2.0
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 = 1st order displacement
1

W
1
Hh
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 = Pf / A
neutral axis
x
fmax = fa + fbx + fby < fdes
fbx = Mfx / Sx
Mfx
( Pf / A ) + ( Mfx / Sx ) + ( Mfy / Sy ) < fdes
x
(Pf / Afdes) + (Mfx / Sxfdes) + (Mfy / Syfdes) < 1.0
fby = Mfy / Sy
y
y
Mfy
(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
 max


1
 0
 
 1  P PE 
M max


1
 M 0
 
 1  P PE 
Δmax
P
PE = Euler load
Interaction equation
 M fy

 M fx 
1
1


 

 1.0
Pr  1  P PEx  M rx  1  P PEy  M ry
Pf
Axial
load
Bending
about x-axis
Bending
about y-axis
3 storey walk-up (woodframe construction)
New Forestry Building, UBC, Vancouver
Stud wall construction
wall and top plate
help to distribute
loads into studs
joists
top plate
wall plate
d
L
studs
check
compression perp.
sill plate