Worked Examples for Timber Beam Design to AS1720.1 Webinar

Created with ClearCalcs.comTimber Beam (version 89) — Roof Bearer
Client: ClearCalcs Date: Mar 11, 2020
Author: Brooks Smith Job #: 12
Project: Webinar Subject: B1
References: AS 1720.1:2010 (Amdt 3)
Moment Demand
Moment Capacity
Governing Load Case for Moment 1.2G, 1.5Q
Shear Demand
Shear Capacity
Governing Load Case for Shear 1.35G
Bearing Demand
Bearing Capacity
Governing Load Case for Bearing 1.35G
Governing Short-Term Deflection
Governing Load Case for Short-Term
Deflection
G, Q_st
Governing Long-Term Deflection
Governing Load Case for Long-Term
Deflection
G
Governing Imposed Load Deflection
Show Plots Including Load Duration
Factor k1?
Graphed Load Case

M =∗
4.06 kN ⋅ m
41% M =d 9.97 kN ⋅ m
M =LC
∗
V =∗
2.45 kN
16% V =d 15.2 kN
V =LC
∗
N =gov
∗
2.45 kN
13% N =d,gov 19.4 kN
N =LC
∗
79% δ =s −7.88 mm
δ =s,LC
97% δ =l −9.74 mm
δ =l,LC
13% δ =Q −1.28 mm
Reactions:
Distance from Left of Beam (m)
0.0 1.0 2.0 3.0
UltMax: 3.23 kN
UltMin: 1.63 kN
G: 3.63 kN
Q: 0.475 kN
UltMax: 3.23 kN
UltMin: 1.63 kN
G: 3.63 kN
Q: 0.475 kN
Yes - Show Final Demands for Individual Load Cases
Service LT: (G)
Load Case: G
Envelope
1.0 2.0 3.0
Shear(kN)
-4
-2
0
2
4
Summary
1

Use Custom Member?
Member Type
Number of Members in Group/Laminate
Total Beam Length
Lateral Restraint Type
Minor Axis Effective Length for Buckling
Position of Supports from Left
Support Type Position ( ) Length of Bearing ( )
Pinned 0 90
Pinned 3 800 90
Maximum Interior Span
Maximum Cantilever
Deflection Limit Absolute Criterion
Load Case: G
Envelope
1.0 2.0 3.0
Moment(kNm)
0.0
1.0
2.0
3.0
4.0
Long-Term LC: G
Envelope 1.0 2.0 3.0
Deflection(mm)
-10
-8
-6
-4
-2
0
Distance from Left of Beam (mm)
0 1,000 2,000 3,000
Self-weight
0.109
0 3 800 mm
0.109 kN/m
Roof Load
1.8
0 3 800 mm
1.8 kN/m
3.63 kN 3.63 kN

d=240mm
b=35 mm
Primary Loading
No
240 x 35 - e-beam (Wesbeam®)
n =com 1
L = 3 800 mm
Discrete Restraints at Compression Edge
L =ay 600 mm
r =
l mm l
b mm
L =maxspan 3 800 mm
L =maxcant 0 mm

Δ =max 10 mm
Key Properties
Design Criteria
2

Deflection Limit Span Criterion
Span Type (Interior or Cantilever) Short-Term Service ( ) Long-Term Service ( ) Imposed Load Q ( )
250 250 250
Structure Category
Distributed Loads
Label Load Width ( ) Permanent Load ( ) Imposed Load ( ) Start Location ( ) End Location ( )
Roof Load 1 000 0.9 0.25 0 3 800
Member Orientation
Self Weight
Include Self Weight
Character of Imposed Load
Wind Class
Ultimate Free Stream Dynamic Pressure
Serviceability Free Stream Dynamic
Pressure

Net Downward Pressure Coefficient
Net Uplift Pressure Coefficient
Wind Tributary/Load Width
Other Point Loads
Label Load Type Magnitude ( ) Location ( )
Alternate Imposed Q2 1.4 1 900
Maximum Beam Depth
Overall Depth
Total Breadth
Gross Area
Shear Plane Area
Second Moment of Area about Relevant
Axis

Section Modulus about Relevant Axis
Elastic Modulus
Stiffness
Axial Stiffness
Timber Density
Timber Member Type LVL
Strength in Bending About Relevant Axis
Strength in Tension Parallel to Grain
Strength in Shear in Beam
Strength in Bearing Perpendicular to
Grain

D =lim
Δ
s,lim L/ Δ
l,lim L/ Δ
Q,lim L/
Interior Spans
2 - Primary Structural Member

w =
mm kPa kPa mm mm
Major Axis
SW = 0.0544 kN/m
Yes
Roofs: All Other

N1
q =u 0.69 kPa
q =s 0.41 kPa
C =pt,down↓ 0.63
C =pt,up↑ −0.99
LW =wind 450 mm
P =other
kN mm

d =max 500 mm
d =total 240 mm
b =total 35 mm
A =g 8 400 mm2
A =s 5 600 mm2
I = 40 300 000 mm4
Z = 336 000 mm3
E = 13 200 MPa
EI = 532 kN ⋅ m2
EA = 111 000 kN
ρ = 660 kg/m3
type =
f =b
′
43.9 MPa
f =t
′
29.9 MPa
f =s
′
5.3 MPa
f =p
′
12 MPa
Permanent and Imposed Loads (AS1170.1)
Wind and Other Loads (AS1170.x)
Member Properties
3

Capacity Factor
Initial Moisture Content Seasoned
Initial Moisture Content from Member
Selection

Equilibrium Moisture Content (Annual
Average)

Partial Seasoning Factor for Bending
Partial Seasoning Factor for Shear
Partial Seasoning Factor for Modulus of
Elasticity

Temperature Factor
Number of Discrete Parallel Members
Geometric Factor in a Combined Parallel
System

Geometric Factor in a Discrete System
Strength Sharing Factor
Slenderness Coefficient
Design Action Ratio
Material Constant in Beams
Stability Factor
Creep Factor Table
Long-Duration Creep ≤1 day 1 week 1 month 3 months ≥1 year
1 1.33 1.58 1.76 2
0.5 0.665 0.788 0.881 1
Creep Factor for Permanent and Long-
Term Imposed Loads

Load Duration Factors
Load Duration: 5 seconds 5 minutes 5 hours 5 days 5 months 50+ years Variable (5d - 5mo)
1 1 0.97 0.94 0.8 0.57 0.94
1 1 1.03 1.06 1.25 1.75 1.06
Character of Imposed Load Factors
Imposed Load Type Short-Term Factor Long-Term Factor Combination Factor Earthquake Factor
0.7 0 0 0
1 0 0 0

ϕ = 0.9
mc =
IMC = 15 %
EMC = 15 %
k =4,M 1
k =4,V 1
j =6 1
k =6 1
1 or 2
g =31 1
g =32 1
k =9 1
S =1 13.6
r =ub 0.25
ρ =b 1.03
k =12 0.799
j =2,table
Factor: j
2
Fraction of max: j /j
2 2,max
j =2,max 2

k =1,table
Factor: k
1
Inverse: 1/k
1
CharQ =
Ψ
s ψ
l Ψ
c Ψ
E
Distributed
Concentrated
Modification Factors (AS1720.1, Cl 2.4)
Load Case Analysis (AS1170.0)
4

Strength Load Cases
Load Case Load Duration Factor Total Load ( ) Shear ( ) Moment ( ) Max Reaction ( )
1.35G 0.57 4.9 -2.45 2.33 2.45
1.2G, 1.5Q 0.94 6.45 -3.23 4.06 3.23
1.2G, 1.5Q_lt 0.57 4.35 -2.18 2.07 2.18
1.2G, Wu_down, Q_comb 1 4.35 -2.18 2.07 2.18
0.9G, Wu_up 1 3.26 -1.63 1.55 1.63
G, Eu, Q_E 1 3.63 -1.81 1.72 1.81
1.2G, Su, Q_comb 0.8 4.35 -2.18 2.07 2.18
Short-term Service Load Cases
Load Case Total Load ( ) Deflection ( )
G, Ws_up 3.63 -4.87
G, Q_st 5.03 -7.88
G, Ws_down, Q_lt 3.63 -4.87
G, Es, Q_lt 3.63 -4.87
G, Ss, Q_lt 3.63 -4.87
Long-term Service Load Cases
G 7.25 -9.74
G, Q_lt 7.25 -9.74
G, Ss, Q_lt 7.25 -9.74
Moment Capacity Excluding Load
Duration Factor

Shear Capacity Excluding Load Duration
Factor

Governing Bearing Capacity Excluding
Load Duration Factor

Strength Load Cases: Demands Divided
by Load Duration Factor
1.35G 0.57 8.59 -4.29 4.08 4.29
1.2G, 1.5Q 0.94 6.86 -3.43 4.32 3.43
1.2G, 1.5Q_lt 0.57 7.63 -3.82 3.63 3.82
1.2G, Wu_down, Q_comb 1 4.35 -2.18 2.07 2.18
0.9G, Wu_up 1 3.26 -1.63 1.55 1.63
G, Eu, Q_E 1 3.63 -1.81 1.72 1.81
1.2G, Su, Q_comb 0.8 5.44 -2.72 2.58 2.72
Load Duration Factor for Governing
Load Case in Moment Demand

Load Case in Shear Demand

Load Case in Bearing Demand

LC =str
k
1 Σw + ΣP kN V ∗
kN M∗
kN ⋅ m N∗
kN
LC =sserv
Σw + ΣP kN Δ
s mm
LC =lserv
Σw + ΣP kN Δ
l mm

M /k =d 1 10.6 kN ⋅ m
V /k =d 1 26.7 kN
N /k =d,gov 1 34 kN
LC /k =str 1
k
1 (Σw + ΣP)/k
1 kN V /k
∗
1 kN M /k
∗
1 kN ⋅ m N /k
∗
1 kN
k =1,M∗ 0.94
k =1,V ∗ 0.57
k =1,N∗ 0.57
Strength Load Case Analysis with Constant Capacity
5

Unfactored Load
Load Type Total Load ( ) Shear ( ) Moment ( ) Max Reaction ( ) Short-Term Deflection ( )
G 3.63 -1.81 1.72 1.81 -4.87
Q 0.95 -0.475 0.451 0.475 -1.28
Bearing Utilisation
Support Location ( ) Bearing Demand ( ) Bearing Factor Bearing Capacity ( ) Bearing Utilisation
0 4.29 1 34 0.126
3 800 4.29 1 34 0.126
Short-Term Deflection Per Span
Span Length ( ) Span Type Short-Term Deflection ( ) Short-term Deflection Limit ( ) Deflection Utilisation
3 800 Int -7.88 10 0.788
Long-Term Deflection Per Span
Span Length ( ) Span Type Long-Term Deflection ( ) Long-term Deflection Limit ( ) Deflection Utilisation
3 800 Int -9.74 10 0.974
Imposed Load Deflection Per Span
Span Length ( ) Span Type Imposed Load Deflection ( ) Imposed Load Deflection Limit ( ) Deflection Utilisation
3 800 Int -1.28 10 0.128
Comments
Beam is not notched
Default equilibrium moisture content is 15% (most non-exposed use)
Default fully-loaded moisture content is less than 25% (most non-exposed use)

Σw + ΣP kN V ∗
kN M∗
kN ⋅ m R∗
kN Δ
s mm

N =d,table
l mm N /k
∗
1 kN k
7 N /k
d 1 kN N /N
∗
d

D =ST
L mm Δ
s mm Δ
s,lim mm Δ /Δ
s s,lim
D =LT
L mm Δ
l mm Δ
l,lim mm Δ /Δ
l l,lim
D =Q
L mm Δ
Q mm Δ
Q,lim mm Δ /Δ
Q Q,lim

1.
2.
3.
Unfactored Load Analysis (AS1170.0)
Bearing Capacity (AS 1720.1:2010, Cl 3.2.6)
Deflection Analysis
Comments
Assumptions
6

Created with ClearCalcs.comTimber Beam (version 89) — Floor Bearer
Client: ClearCalcs Date: Mar 11, 2020
Author: Brooks Smith Job #: 12
Project: Webinar Subject: B2
References: AS 1720.1:2010 (Amdt 3)
Moment Demand
Moment Capacity
Governing Load Case for Moment 1.2G, 1.5Q
Shear Demand
Shear Capacity
Governing Load Case for Shear 1.2G, 1.5Q
Bearing Demand
Bearing Capacity
Governing Load Case for Bearing 1.2G, 1.5Q
Governing Short-Term Deflection
Governing Load Case for Short-Term
Deflection
G, Q_st
Governing Long-Term Deflection
Governing Load Case for Long-Term
Deflection
G, Q_lt
Governing Imposed Load Deflection
Show Plots Including Load Duration
Factor k1?
Graphed Load Case

M =∗
−15.2 kN ⋅ m
32% M =d 48.2 kN ⋅ m
M =LC
∗
V =∗
17.8 kN
32% V =d 55.1 kN
V =LC
∗
N =gov
∗
33.2 kN
37% N =d,gov 90.9 kN
N =LC
∗
65% δ =s −6.49 mm
δ =s,LC
93% δ =l −9.32 mm
δ =l,LC
62% δ =Q −6.17 mm
Reactions:
Distance from Left of Beam (m)
0 2 4 6 8 10
UltMax: 5.24 kN
UltMin: 1.42 kN
G: 3.17 kN
Q: 2.23 kN
UltMax: 33.2 kN
UltMin: 6.65 kN
G: 14.8 kN
Q: 16.3 kN
UltMax: 23.6 kN
UltMin: 4.2 kN
G: 9.33 kN
Q: 12 kN
No - Show Envelope Plots Divided by k1
Strength: (1.2G, 1.5Q)
Load Case: 1.2G, 1.5Q
Envelope
2 4 6 8 10
Shear(kN)
-20
-10
0
10
20
Summary
7

Use Custom Member?
Timber Grade
Timber Species
Depth of Custom Section
Breadth of Single Member/Laminate in
Custom Member

Number of Members in Group/Laminate
Total Beam Length
Lateral Restraint Type
Minor Axis Effective Length for Buckling
Position of Supports from Left
Support Type Position ( ) Length of Bearing ( )
Pinned 0 90
Pinned 3 000 90
Pinned 8 500 90
Maximum Interior Span
Maximum Cantilever
Deflection Limit Absolute Criterion
Load Case: 1.2G, 1.5Q
Envelope
2 4 6 8 10
Moment(kNm)
-20
-10
0
10
Distance from Left of Beam (mm)
0 2,000 4,000 6,000 8,000 10,000
Self-weight
0.273
0 10 000 mm
0.273 kN/m
Floor Load
7.13
0 10 000 mm
7.13 kN/m
B1-2
3.61 kN
Alternate Imposed
3.38 kN
6.55 kN 41.6 kN 29.5 kN

width=135 mm
height=250mm
Primary Loading
Yes
F17
Pine, Radiata (Australia & New Zealand, heart-in
material included) - Seasoned
d = 250 mm
b = 45 mm
n =com 3
L = 10 000 mm
Discrete Restraints at Compression Edge
L =ay 450 mm
r =
l mm l
b mm
L =maxspan 5 500 mm
L =maxcant 1 500 mm

Δ =max 10 mm
Key Properties
Design Criteria
8

Deflection Limit Span Criterion
Span Type (Interior or Cantilever) Short-Term Service ( ) Long-Term Service ( ) Imposed Load Q ( )
300 300 300
150 150 150
Structure Category
Distributed Loads
Label Load Width ( ) Permanent Load ( ) Imposed Load ( ) Start Location ( ) End Location ( )
Floor Load 2 000 0.5 1.5 0 10 000
Point Loads
Label Permanent Load ( ) Imposed Load ( ) Location ( )
B1-2 1.81 0.475 1 500
Member Orientation
Self Weight
Include Self Weight
Character of Imposed Load
Wind Class
Ultimate Free Stream Dynamic Pressure
Serviceability Free Stream Dynamic
Pressure

Net Downward Pressure Coefficient
Net Uplift Pressure Coefficient
Wind Tributary/Load Width
Other Point Loads
Label Load Type Magnitude ( ) Location ( )
Alternate Imposed Q2 1.8 10 000
Maximum Beam Depth
Overall Depth
Total Breadth
Gross Area
Shear Plane Area
Second Moment of Area about Relevant
Axis

Section Modulus about Relevant Axis
Elastic Modulus
Stiffness
Axial Stiffness
Timber Density
Timber Member Type Sawn High Grade
Strength in Bending About Relevant Axis
Strength in Tension Parallel to Grain
D =lim
Δ
s,lim L/ Δ
l,lim L/ Δ
Q,lim L/
Interior Spans
Cantilevers
2 - Primary Structural Member

w =
mm kPa kPa mm mm
P =
kN kN mm
Major Axis
SW = 0.182 kN/m
Yes
Floors: Residential and Domestic

N1
q =u 0.69 kPa
q =s 0.41 kPa
C =pt,down↓ 0
C =pt,up↑ 0
LW =wind 450 mm
P =other
kN mm

d =max 500 mm
d =total 250 mm
b =total 135 mm
A =g 33 800 mm2
A =s 22 500 mm2
I = 176 000 000 mm4
Z = 1 410 000 mm3
E = 14 000 MPa
EI = 2 460 kN ⋅ m2
EA = 473 000 kN
ρ = 550 kg/m3
type =
f =b
′
42 MPa
f =t
′
22 MPa
Permanent and Imposed Loads (AS1170.1)
Wind and Other Loads (AS1170.x)
Member Properties
9

Strength in Shear in Beam
Strength in Bearing Perpendicular to
Grain

Capacity Factor
Initial Moisture Content Seasoned
Initial Moisture Content from Member
Selection

Equilibrium Moisture Content (Annual
Average)

Partial Seasoning Factor for Bending
Partial Seasoning Factor for Shear
Partial Seasoning Factor for Modulus of
Elasticity

Temperature Factor
Number of Discrete Parallel Members
Geometric Factor in a Combined Parallel
System

Geometric Factor in a Discrete System
Strength Sharing Factor
Slenderness Coefficient
Design Action Ratio
Material Constant in Beams
Stability Factor
Creep Factor Table
Long-Duration Creep ≤1 day 1 week 1 month 3 months ≥1 year
1 1.33 1.58 1.76 2
0.5 0.665 0.788 0.881 1
Creep Factor for Permanent and Long-
Term Imposed Loads

Load Duration Factors
Load Duration: 5 seconds 5 minutes 5 hours 5 days 5 months 50+ years Variable (5d - 5mo)
1 1 0.97 0.94 0.8 0.57 0.8
1 1 1.03 1.06 1.25 1.75 1.25
Character of Imposed Load Factors
Imposed Load Type Short-Term Factor Long-Term Factor Combination Factor Earthquake Factor
0.7 0.4 0.4 0.3
1 0.4 0.4 0.3
f =s
′
3.6 MPa
f =p
′
10 MPa

ϕ = 0.85
mc =
IMC = 15 %
EMC = 15 %
k =4,M 1
k =4,V 1
j =6 1
k =6 1
1 or 2
g =31 1.2
g =32 1.2
k =9 1.2
S =1 3.11
r =ub 0.25
ρ =b 0.985
k =12 1
j =2,table
Factor: j
2
Fraction of max: j /j
2 2,max
j =2,max 2

k =1,table
Factor: k
1
Inverse: 1/k
1
CharQ =
Ψ
s ψ
l Ψ
c Ψ
E
Distributed
Concentrated
Modification Factors (AS1720.1, Cl 2.4)
Load Case Analysis (AS1170.0)
10

Strength Load Cases
1.35G 0.57 18.4 -5.1 -4.44 9.97
1.2G, 1.5Q 0.8 62.1 17.8 -15.2 33.2
1.2G, 1.5Q_lt 0.57 34.6 9.73 -8.47 18.6
1.2G, Wu_down, Q_comb 1 28.6 7.93 -6.96 15.4
0.9G, Wu_up 1 12.3 -3.4 -2.96 6.65
G, Eu, Q_E 1 22.8 6.31 -5.55 12.3
1.2G, Su, Q_comb 0.8 28.6 7.93 -6.96 15.4
Short-term Service Load Cases
G, Ws_up 13.6 -2.19
G, Q_st 35.1 -6.49
G, Ws_down, Q_lt 25.8 -4.66
G, Es, Q_lt 25.8 -4.66
G, Ss, Q_lt 25.8 -4.66
Long-term Service Load Cases
G 27.3 -4.38
G, Q_lt 51.6 -9.32
G, Ss, Q_lt 51.6 -9.32
Moment Capacity Excluding Load
Duration Factor

Shear Capacity Excluding Load Duration
Factor

Governing Bearing Capacity Excluding
Load Duration Factor

Strength Load Cases: Demands Divided
by Load Duration Factor
1.35G 0.57 32.3 -8.94 -7.79 17.5
1.2G, 1.5Q 0.8 77.6 22.3 -19.1 41.6
1.2G, 1.5Q_lt 0.57 60.8 17.1 -14.9 32.7
1.2G, Wu_down, Q_comb 1 28.6 7.93 -6.96 15.4
0.9G, Wu_up 1 12.3 -3.4 -2.96 6.65
G, Eu, Q_E 1 22.8 6.31 -5.55 12.3
1.2G, Su, Q_comb 0.8 35.7 9.91 -8.7 19.2
Load Case in Moment Demand

Load Case in Shear Demand

Load Case in Bearing Demand

LC =str
k
1 Σw + ΣP kN V ∗
kN M∗
kN ⋅ m N∗
kN
LC =sserv
Σw + ΣP kN Δ
s mm
LC =lserv
Σw + ΣP kN Δ
l mm

M /k =d 1 60.2 kN ⋅ m
V /k =d 1 68.9 kN
N /k =d,gov 1 114 kN
LC /k =str 1
k
1 (Σw + ΣP)/k
1 kN V /k
∗
1 kN M /k
∗
1 kN ⋅ m N /k
∗
1 kN
k =1,M∗ 0.8
k =1,V ∗ 0.8
k =1,N∗ 0.8
Strength Load Case Analysis with Constant Capacity
11

Unfactored Load
Load Type Total Load ( ) Shear ( ) Moment ( ) Max Reaction ( ) Short-Term Deflection ( )
G 13.6 -3.78 -3.29 7.38 -2.19
Q 30.5 9.01 -7.53 16.3 -6.17
Bearing Utilisation
Support Location ( ) Bearing Demand ( ) Bearing Factor Bearing Capacity ( ) Bearing Utilisation
0 6.55 1 103 0.0634
3 000 41.6 1.1 114 0.366
8 500 29.5 1.1 114 0.26
Short-Term Deflection Per Span
Span Length ( ) Span Type Short-Term Deflection ( ) Short-term Deflection Limit ( ) Deflection Utilisation
3 000 Int -0.381 10 0.0381
5 500 Int -6.49 10 0.649
1 500 Cant 4.1 10 0.41
Long-Term Deflection Per Span
Span Length ( ) Span Type Long-Term Deflection ( ) Long-term Deflection Limit ( ) Deflection Utilisation
3 000 Int -0.542 10 0.0542
5 500 Int -9.32 10 0.932
1 500 Cant 5.87 10 0.587
Imposed Load Deflection Per Span
Span Length ( ) Span Type Imposed Load Deflection ( ) Imposed Load Deflection Limit ( ) Deflection Utilisation
3 000 Int 0.516 10 0.0516
5 500 Int -6.17 10 0.617
1 500 Cant 3.92 10 0.392
Comments
Beam is not notched
Default equilibrium moisture content is 15% (most non-exposed use)
Default fully-loaded moisture content is less than 25% (most non-exposed use)

Σw + ΣP kN V ∗
kN M∗
kN ⋅ m R∗
kN Δ
s mm

N =d,table
l mm N /k
∗
1 kN k
7 N /k
d 1 kN N /N
∗
d

D =ST
L mm Δ
s mm Δ
s,lim mm Δ /Δ
s s,lim
D =LT
L mm Δ
l mm Δ
l,lim mm Δ /Δ
l l,lim
D =Q
L mm Δ
Q mm Δ
Q,lim mm Δ /Δ
Q Q,lim

1.
2.
3.
Unfactored Load Analysis (AS1170.0)
Bearing Capacity (AS 1720.1:2010, Cl 3.2.6)
Deflection Analysis
Comments
Assumptions
12

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