CH12AnalysisofIndeterminateBeamsandFramesbytheSlope-DeflectionMethod.ppt

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CH12AnalysisofIndeterminateBeamsandFramesbytheSlope-DeflectionMethod.ppt

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CH12AnalysisofIndeterminateBeamsandFramesbytheSlope-DeflectionMethod

上一页下一页回目录 Express member end moments in terms of displacements 12.5 Analysis of Structures That Are Free to Sidesway Solution Write the joint equilibrium equations at B and C. Joint B (see Fig. 12.16b): 上一页下一页回目录 12.5 Analysis of Structures That Are Free to Sidesway Solution Joint C (see Fig. 12.16c): Shear equation (see Fig. 12.16d): Solving for V1 gives 上一页下一页回目录 12.5 Analysis of Structures That Are Free to Sidesway Solution Isolate the girder and consider equilibrium in the horizontal direction. Substitute Equation 4a into Equation 4b: Express equilibrium equations in terms of displacements by substituting equations 1 into equations 2, 3, and 4. Collecting terms and simplifying, we find 上一页下一页回目录 12.5 Analysis of Structures That Are Free to Sidesway Solution Solution of the equations above gives Establish the values of member end moments by substituting the values of θB, θC, and ψAB into Equations 1. 上一页下一页回目录 After the end moments are established, we compute the shears in all members by applying the equations of equilibrium to free bodies. Final results are shown in Figure 12.16f. 12.5 Analysis of Structures That Are Free to Sidesway Solution 上一页下一页回目录 Unknown displacements are θB, θC, and c. Since supports at A are fixed, θA and θD equal zero. There is no chord rotation of girder BC. 12.5 Analysis of Structures That Are Free to Sidesway Analyze the frame by the slope-deflection method. Determine the reactions, draw the moment curves for the members, and sketch the deflected shape. If I = 240 in4 and E = 30,000 kips/in2, determine the horizontal displacement of joint B. Example 12.8 Solution 上一页下一页回目录 Express member end moments in terms of displacements with the slope-deflection equation. Use Figure 12.5 to evaluate FEMNF. To simplify slope-deflection expressions, set EI/15 =K, then 12.5 Analysis of Structures That Are Free to Sidesway solution 上一页下一页回目录 12.5 Analysis of Structures That Are Free to Sidesway Solution 上一页下一页回目录 The equil