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