design of concrete & masonry

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Design of Concrete & MasonryStructures

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 movementor temperature gradient, which may act on a structure.

• Action effects

The forces and moments, deformations, cracks and othereffects, which are produced in a structure or in its

component members by an action.

• Load path

How the externally applied loads are transferred throughthe 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?

StrengthStrength varies between batches

Histogram

0

10

20

30

40

50

60

70

80

40 45 50 55 60 65 70

Strength (MPa)

N u m b e r o f S p e c i m e n 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 MPa

B. 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 Load

B. Characteristic Load = Mean Load

C. 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 direction

wu = 0.9 G

G = Dead LoadQ = Live Load

DL LL

4 0 0

2 0 0

L = 6000 mm a = 2000 mm

Concrete Density = 24 kN/m3Additional Imposed Dead Load = 1 kPa

Live Load = 3 kPa



Maximum Factored Design Load,Fd

A. between 35 to 40 kN/mB. between 40 to 45 kN/m

C. between 45 to 50 kN/m

D. between 50 to 55 kN/m

E. between 55 to 60 kN/m

F. 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 kNm

Moment 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)

Factored

Positive

Moment at B

110.88*1.2 54*1.5 -24.64*0.9 -12*0

Total: 191.88 kNm

Factored

Negative

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, considerationsfor (live load, imposed dead load and load factor)



Design moment, M*B = ?

A. between 40 to 70 kNmB. between 70 to 100 kNm

C. between 100 to 130 kNm

D. between 130 to 160 kNm

E. between 160 to 190 kNm

F. between 190 to 220 kNm

Design moment, M*C = ?

A. between 40 to 70 kNmB. between 70 to 100 kNm

C. between 100 to 130 kNm

D. between 130 to 160 kNm

E. between 160 to 190 kNm

F. between 190 to 220 kNm

MB is not the maximum positive moment now !

Mmax.

Strength Check

Rd >= Ed (Design capacity >= Design actioneffects)

Rd = φ Ru = Design action effects due to designload

Ru = ultimate strength (bending, shear, ..)

φ = Strength reduction factors

φ, strength reduction factors• Bending = 0.8

• Shear = 0.7

• Axial compression = 0.6

Practice SetNext Week

Complex combinationof Loads ! # ?

How to get the actioneffects ! # ?



25

Structural Analysis

• Structural analysis of buildings may be carried outusing the advanced computer-based method.

26

Three-Dimensional FiniteElement Analysis

27

Three-Dimensional Frame Analysis

28

Two-Dimensional Frame Analysis

29

Two-DimensionalFrame 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 forcontinuous beams subject to the following

restrictions:

- Spans are approximately equal with the larger of twoadjacent 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 design

Long term load, w = G + ψl Q

Short term load, w = G + ψs Q

(HB 2.2-2003, pp 492)

G = Dead Load

Q = Live Load

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