1. “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( )
Satyam Bhimani( )
Vidhi Patel( )
Prachi Shah( )
Guided By,
Samir Gami
Asst. Prof. of Civil Engginerring
NSIT, Jetalpur

2. 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.

3. 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.

4. ( 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

5. 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)

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

7. 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

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

10. 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

13. Thank You