Advanced Methods of Structural Analysis

Chapter 2 General Theory of Influence Lines Construction of influence lines for one span simply supported and cantilevered beams ...

16 2 General Theory of Influence Lines only that position of the load is arbitrary, i.e., this is astaticload, which may have di ...

2.1 Analytical Method for Construction of Influence Lines 17 Fig. 2.1 Simply supported beam. Influence lines for reactions P= 1 ...

18 2 General Theory of Influence Lines Influence Line forRB Equilibrium equation in form of moments of all the external forces a ...

2.1 Analytical Method for Construction of Influence Lines 19 Influence lines of reactions are shown in Fig.2.2.IfloadPD 1 is sit ...

20 2 General Theory of Influence Lines SincePD 1 , the equation of influence line becomes IL.RA/D1: (2.4) It means that reaction ...

2.1 Analytical Method for Construction of Influence Lines 21 bending moment is Mk! X MkrightD 0 W MkDRBb: If position of the lo ...

22 2 General Theory of Influence Lines As above, the expression for bending moment is transformed to the equation of influence l ...

2.1 Analytical Method for Construction of Influence Lines 23 LoadPD 1 left at sectionk LoadPD 1 right at sectionk Qk! P YrightD ...

24 2 General Theory of Influence Lines Fig. 2.6 Beam with overhangs. Construction of influence lines for bending moment and shea ...

2.1 Analytical Method for Construction of Influence Lines 25 Ta b l e 2. 1 Comparison of influence line for bending moment and b ...

26 2 General Theory of Influence Lines Fig. 2.9 Construction of influence lines for section 2 on the overhang P= 1 2 x c The inf ...

2.2 Application of Influence Lines for Fixed and Moving Loads 27 2.2 Application of Influence Lines for Fixed and Moving Loads I ...

28 2 General Theory of Influence Lines Uniformly Distributed Load Value of any functionZdue to action of uniformly distributed l ...

2.2 Application of Influence Lines for Fixed and Moving Loads 29 The value of reactionRAdue to given fixed loadsP,q,andMequals R ...

30 2 General Theory of Influence Lines If loadP 1 is located to therightat sectionn,then QnD 12 0:4C 8 .0:3/C 3 .1:8/C 2 . ...

2.2 Application of Influence Lines for Fixed and Moving Loads 31 In case of set of concentrated moving loads, we assume that som ...

32 2 General Theory of Influence Lines Influence Line Forms a Polygon A dangerous position of the set of moving concentrated loa ...

2.3 Indirect Load Application 33 P 1 P 1 P 1 P 1 P 1 P 2 2m q 3m 6m 4m 3m k A B Inf. line Mk (m) 2.4 − + 0.6 1.8 1.6 1.2 Inf. li ...

34 2 General Theory of Influence Lines Fig. 2.15 Indirect load application Inf. line Z A d B P= 1 m n Main beam Stringer Floor b ...