Design of Concrete & Masonry Structures Dr. Barry Y. Bai Lecture #2 (week 2) 30.07.2010 CIV2226 1 Previously on this topic… • Actions Any agent, such as imposed load, foundation movement or temperature gradient, which may act on a structure. • Action effects The forces and moments, deformations, cracks and other effects, which are produced in a structure or in its component members by an action. • Load path How the externally applied loads are transferred through the member and into its supports 2 Feedbacks • Lab groups 3 • Revision Chapter 2, Textbook Strength Check Serviceability Check Is the structure strong enough ? Is the structure stiff enough? Strength Strength varies between batches Histogram 0 10 20 30 40 50 60 70 80 40 45 50 55 60 65 70 Strength (MPa) Number of Specimens
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Design of Concrete & Masonry Structures
Dr. Barry Y. BaiLecture #2 (week 2)
30.07.2010
CIV2226
1
Previously on this topic…• Actions
Any agent, such as imposed load, foundation movement or temperature gradient, which may act on a structure.
• Action effectsThe forces and moments, deformations, cracks and other effects, which are produced in a structure or in its component members by an action.
• Load pathHow the externally applied loads are transferred through the member and into its supports
2
Feedbacks• Lab groups
3
• Revision
Chapter 2, Textbook
Strength Check
Serviceability Check
Is the structure strong enough ?
Is the structure stiff enough?
Strength
Strength varies between batches
Histogram
0
10
20
30
40
50
60
70
80
40 45 50 55 60 65 70
Strength (MPa)
Nu
mb
er
of S
pe
cim
en
s
Strength
Probability
Mean, fcmf 'c
f 'c = Characteristic Strength f cm = Mean Strength
5%
Loads
Loads
Probability
Mean
Characteristic Load
Which one is correct?
A. f cm = 40 MPa and f 'c = 45 MPaB. f cm = 40 MPa and f 'c = 40 MPa C. f cm = 45 MPa and f 'c = 40 MPa
20 seconds to answer
Which one is correct?
A. Characteristic Load > Mean LoadB. Characteristic Load = Mean LoadC. Characteristic Load < Mean Load
20 seconds to answer
Load Factors – Strength Design
wu =1.2 G + 1.5 Q
If loads are in the helping directionwu = 0.9 G
G = Dead LoadQ = Live Load
DL LL
400
200
L = 6000 mm a = 2000 mm
Concrete Density = 24 kN/m3Additional Imposed Dead Load = 1 kPaLive Load = 3 kPa
Maximum Factored Design Load, Fd
A. between 35 to 40 kN/mB. between 40 to 45 kN/mC. between 45 to 50 kN/mD. between 50 to 55 kN/m
E. between 55 to 60 kN/mF. between 60 to 65 kN/m
• Action effects: BMD
A B C D
Un-factored Load only on AC span (WB)
Load only on CD span (WC)
Dead load WGB (24.64 kN/m)
Live load WGB (12 kN/m)
Dead load WGC (24.64 kN/m)
Live load WGC (12 kN/m)
Moment at B (kNm) Factored total: 110.88*1.2+54*1.5-24.64*1.2-
12*1.5=166.49 kNmMoment at C (kNm) Factored total: -49.28*1.2-24*1.5=-95.14 kNm
1.2 G + 1.5 Q
Load only on AC span (WB) Load only on CD span (WC)
Un-factored Dead load WGB
(24.64 kN/m)
Un-factored Live load WQB
(12 kN/m)
Un-factored Dead load WGC
(24.64 kN/m)
Un-factored Live load WGC
(12 kN/m)FactoredPositive Moment at B
110.88*1.2 54*1.5 -24.64*0.9 -12*0
Total: 191.88 kNm
FactoredNegative Moment at C
0 0 -49.28*1.2 -24*1.5
Total: 95.14 kNm
The case if loads are in the helping direction, considerations for (live load, imposed dead load and load factor)
Design moment, M*B = ?
A. between 40 to 70 kNmB. between 70 to 100 kNmC. between 100 to 130 kNmD. between 130 to 160 kNm
E. between 160 to 190 kNmF. between 190 to 220 kNm
Design moment, M*C = ?
A. between 40 to 70 kNmB. between 70 to 100 kNmC. between 100 to 130 kNmD. between 130 to 160 kNm
E. between 160 to 190 kNmF. between 190 to 220 kNm
MB is not the maximum positive moment now !
Mmax.
Strength Check
Rd >= Ed (Design capacity >= Design action effects)
Rd = φ Ru = Design action effects due to design load
Ru = ultimate strength (bending, shear, ..)
φ = Strength reduction factors
φ, strength reduction factors
• Bending = 0.8• Shear = 0.7• Axial compression = 0.6
Practice Set Next Week
Complex combination of Loads ! # ? �
How to get the action effects ! # ? �
25
Structural Analysis
• Structural analysis of buildings may be carried out using the advanced computer-based method.
26
Three-Dimensional Finite Element Analysis
27
Three-Dimensional Frame Analysis
28
Two-Dimensional Frame Analysis
29
Two-Dimensional Frame Analysis
Bending moments in beams and columns 30
Simplified Method of Analysis of Continuous Beams
• Clause 7.2.1 of AS 3600 allows the use of approximate moment and shear coefficients for continuous beams subject to the following restrictions:
- Spans are approximately equal with the larger of two adjacent spans not exceeding the shorter by more than 20 %.
- Loads are uniformly distributed.- Unit live load q does not exceed twice the unit dead load g.- Members are of uniform cross section.
31
Two spans
Moment = Coef. * Fd Ln2 32
More than two spans
Moment = Coef. * Fd Ln2
AS3600 p.62
Rd >= Ed (Design capacity >= Design action effects)
Rd = φφφφ Ru
Serviceability Check
• Deflections• Crack widths
Serviceability designLong term load, w = G + ψl QShort term load, w = G + ψs Q
(HB 2.2-2003, pp 492)
G = Dead LoadQ = Live Load
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