Presentation on theme: "CIVL3310 STRUCTURAL ANALYSIS"— Presentation transcript:
1CIVL3310 STRUCTURAL ANALYSIS Chapter 6:Influence Lines for Statically Determinate StructuresCIVL3310 STRUCTURAL ANALYSISProfessor CC Chang
2Why Influence Lines? Vmax and Mmax under dead & live loads? ConcentratedLive LoadConcentratedLive LoadConcentratedLive LoadwPDistributed Live LoadDistributed Live LoadDistributed Live LoadDead LoadABCDVMAnalysisw, PV, MDesignNote: loads can vary- LIVE LOADSVmax and Mmax under dead & live loads?
8Influence Lines Shear force and moment diagrams Fixed loads V M x V and M at different locations of the beamxInfluence LinesLoad moves along the beamVMxxV and M at a fixed location
9Influence Lines Influence line: A graph of a response function (such as reactions or internal forces) of a structure as a function of the position of a downward unit load moving across the structureResponseLocation of downward unit load
13Influence LinesAll statically determinate structures have influence lines that consist of straight line segmentsMore examples!
14Müller Breslau Principle Influence line for any action (reaction, internal shear/moment) in a structure is equal to the deflection curve when we remove the action and replace it with a corresponding unit displacement or rotationInfluence line = properly disturbed shape
16Virtual work principle for a rigid-body system Virtual deformationA structure in equilibrium:imaginary deformationResultant force=0Virtual work:Virtual work principle for a rigid-body system
17Müller Breslau Principle Influence line = properly disturbed shapex1AyBy1Ay1Ay1f(x)ByInfluence line of AyVirtual work
18Müller Breslau Principle Influence line = properly disturbed shapex1AyBy1By1ByInfluence line of By1f(x)AyVirtual work
19Müller Breslau Principle Influence line = properly disturbed shapeInclude ONLY the reaction/force in the virtual workx1VAyByVMf(x)1D21q2q1AyD1ByMV=1=
20Müller Breslau Principle Influence line = properly disturbed shapeInclude ONLY the reaction/force in the virtual workx1MAyByVMf(x)1D1q1q2AyBy=1
21Müller Breslau Principle Influence line = properly disturbed shapeDeflect the structure such that only the force which influence line that you are looking for and the downward unit force contribute to the virtual work due to the imaginary deflection.All other forces that act on the virtually deflected structure should not contribute to the virtual work.
22Influence Lines for Floor Girders Draw the influence line for the shear in panel CD of the floor girder