Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
1
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern loading
TABLE OF CONTENTS
STRUCTURAL ANALYSIS ................................................................................................................................... 2
THE REAL BUILDING ........................................................................................................................................ 2
THREE-DIMENSIONAL FINITE ELEMENT ANALYSIS .......................................................................................... 2
THREE-DIMENSIONAL FRAME ANALYSIS ......................................................................................................... 3
TWO-DIMENSIONAL FRAME ANALYSIS ............................................................................................................ 3
CONTINUOUS BEAM ANALYSIS ........................................................................................................................ 5
PATTERN LOADING, MOMENT ENVELOPES....................................................................................................... 5
Full live load on all spans............................................................................................................................ 5
Live load pattern for maximum interior support moment............................................................................ 5
Live load pattern for maximum outer spans positive moment ..................................................................... 6
Live load pattern for maximum inner span positive moment ....................................................................... 6
AS3600 CODE PROVISIONS FOR LIVE LOAD PATTERN LOADING ..................................................................... 6
SIMPLIFIED METHOD OF ANALYSIS OF CONTINUOUS BEAMS ........................................................................... 7
Two Spans.................................................................................................................................................... 7
More than two Spans ................................................................................................................................... 8
ANALYSIS OF BAND BEAM FLOOR ................................................................................................................... 9
Department of Civil Engineering, Monash University
Edition Date: 9/2003
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
2
Structural Analysis
Analysis of the building may be carried out using the advanced computer-based stiffness
method. In performing the analysis, a number of analysis schemes may be considered.
These are listed in decreasing levels f complexity:
The Real Building
Three-Dimensional Finite Element Analysis
Department of Civil Engineering, Monash University
Edition Date: 9/2003
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
Three-Dimensional Frame Analysis
Two-Dimensional Frame Analysis
Department of Civil Engineering, Monash University
Edition Date: 9/2003
3
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
4
gravity loads on beams
Bending moments in beams and
columns
Department of Civil Engineering, Monash University
Edition Date: 9/2003
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
5
Continuous Beam Analysis
The analysis of the building may be carried out level-by-level by considering the continuous
beam components. Analysis of continuous beams may be carried out using the advanced
computer-based stiffness method. In performing the analysis, several load cases and
combinations must be considered to determine the maximum effects (envelopes) at various
parts of the beam. The following illustrates the load cases required to determine the
maximum bending moments in a three-span continuous beam.
Pattern Loading, Moment Envelopes
Full live load on all spans
Live load pattern for maximum interior support moment
Department of Civil Engineering, Monash University
Edition Date: 9/2003
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
6
Live load pattern for maximum outer spans positive moment
Live load pattern for maximum inner span positive moment
AS3600 Code Provisions for Live Load Pattern Loading
The Australian concrete code AS 3600 specifies the following load cases to be considered to
obtain maximum bending moments (see section 7.6.4 of the Australian Standards for Civil
Engineering Students SAA HB2.2-1995):
Live load does not exceed three-quarters of the dead load:
Consider all spans to be loaded (no need to consider pattern live loads). This means that
only load cases 1 and 2 and load combination I below should be considered.
Live load exceeds three-quarters of the dead load:
Consider pattern live loads as follows:
a) For maximum positive moments in spans, alternate spans loaded with all other
spans unloaded.
b) To obtain maximum negative support moments, any two adjacent spans loaded.
c) All spans loaded
Department of Civil Engineering, Monash University
Edition Date: 9/2003
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
7
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 and one-way slabs subject to the following restrictions:
1)
Spans are approximately equal with the larger of two adjacent spans not
exceeding the shorter by more than 20 %.
2)
Loads are uniformly distributed.
3)
Unit live load q doesnot exceed twice the unit dead load g.
4)
Members are of uniform cross section.
Mom
= Coef. * Fd Ln2
Two Spans
0
-1/16
-1/9
+1/11
+1/11
brick wall
RC column
Ln
Ln
0
-1/24
-1/9
+1/11
brick wall
RC column
+1/11
RC column
Department of Civil Engineering, Monash University
Edition Date: 9/2003
RC beam
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
8
More than two Spans
-1/11
-1/10
0
brick wall
RC column
+1/11
brick wall
+1/16
RC column
+1/11
RC column
-1/11
-1/10
0
+1/16
+1/16
+1/11
-1/16
-1/10
RC column
-1/24
-1/10
+1/16
RC column
Department of Civil Engineering, Monash University
Edition Date: 9/2003
RC column
RC beam
+1/11
RC column
Subject CIV2223 Design of Concrete Structures
Structural Analysis: Frames, Continuous Beams, Load cases, Pattern Loading
9
Analysis of Band Beam Floor
A
B
C
D
E
50 0 x 450
3 0 m m M A T S E TD OWN
3000
WE S TE RN
B RID G E
630 x 450
1
2
900
3
50 0 x 450
S OUTH E RN
B RID G E
Ds
D
bw
L = 7.5 m
3000
20
0
450
500
400
450
450
9000
450
9000
Department of Civil Engineering, Monash University
Edition Date: 9/2003