“ENERGY PRINCIPLE:UNIT LOAD FOR DETERMINATE STRUCTURE” Narnarayan Shastri Institute of Technology STRUCTURE ANALYSIS-ǁ “ENERGY PRINCIPLE:UNIT LOAD FOR DETERMINATE STRUCTURE” Prepared by, Harsh Patel(130340106064) Satyam Bhimani(130340106073) Vidhi Patel(130340106079) Prachi Shah(130340106084) Guided By, Samir Gami Asst. Prof. of Civil Engginerring NSIT, Jetalpur

Energy principle of unit load for determinate structure δ= ……deflection   Ѳ = …………Slope Where, M=moment at section X due to applied load m=Moment at section X due to unit force or unit moment.

Example 1:compute deflection at point C of cantilever beam shown in the figure. For the beam E= I = Solution : To find deflection at C. apply unit load 1 kN at C.

( Segment ORIGIN Limits M m BC B 0 to 3 CA C 0 to 3 -20(x+3) -1(x) CA C 0 to 3 -20(x+3) -1(x) ( =7.5 mm

Example 2: Determine deflection at free end of a cantilever beam using unit load method. Solution: Segment ORIGIN Limits M m BC B 0 to 4 -20x CA C 0 to 4 -20(x+3) -1(x)

To find deflection at C. apply unit load 1 kN at C.

Example: 3 Determinate deflection at the free end C of a beam ABC shawn in figure.Take   Segment Origin Limits M m AD A 0 to 4 10x -0.25x DB D 10(x-4)-30x -0.25(x+4) CB C 0 to 2 -20x -1.x

Solution: Taking moments about A. To find δ,apply unit load at C

Example 4: Find vertical and horizontal displacement at C for a cantilever frame using unit load method. Solution: Segment Origin Limits M m1 m2 I CB C 0 to 2 -1 x BA B 0 to 6 -4 x 2 x 1 -2 -1x 2I

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