1. Standard Cases for Slope and Deflection (SSB)
Lecture No-3
J P Supale
Mechanical Engineering Department
SKN SITS LONAVALA
Strength of Materials

2. Standard Cases
SSB with point loads
SSB with UDL
Strength of Materials

3. 1. SSB with point loads Step 1- Calculate the reaction at supports.
Ler RA be the reaction at support A and RB be the
reaction at support B.
RA = RB = W A B
L/4
L/2
L/4 L
Strength of Materials

4. SSB with Point Loads
Step 2 - Take a section X-X at a distance X from left end A W W A B
L/4
L/2
L/4 L X
Strength of Materials

5. SSB with Point Loads
Step 3 - Take moment of all forces about section x-x Step 4 – Separate the moment of each force by using compartment line
Strength of Materials

6. SSB with Point Loads
Step 5 – Use the differential deflection equation Step 6 – Equate the left hand side of it with step 5 equation
Strength of Materials

7. SSB with Point Loads Step 7- Integrate Step 8- Again integrate
Strength of Materials

8. SSB with Point Loads
Step 9- Apply BCs, at x=0, y=0, we get Put x=L, y=0 , we get Step 10- Put Values of C1 and C2 in Step 7 and Step 8 to get Slope and Deflection equation
Strength of Materials

9. SSB with Point Loads Slope Equation Deflection Equation
Strength of Materials

10. SSB with Point Loads
Slope at A, Put x=0 in slope eq. Slope at B, Put x=L Deflection at centre, put x=L/2, in deflection eq.
Strength of Materials

11. 2. SSB with UDL Step 1- Calculate Reaction, RA=RB=WL/2 L W A B
Strength of Materials

12. SSB with UDL X Step 2- Take a section X-X at distance X from left end
Strength of Materials

13. SSB with UDL
Step 3- Taking moment of all forces about Section X and equating it with Differential Deflection equation Step 4- Integrate
Strength of Materials

14. SSB with UDL
Step 5 – Again Integrate Step 6 – Applying Boundary conditions, when x=0, y=0 in step 5, we get Put x=L, y=0, we get
Strength of Materials

15. SSB with UDL
Step 7- put values of C1 and C2 in step 4 and 5 to get Slope and Deflection equation Slope Equation Deflection Equation
Strength of Materials

16. SSB with UDL
Slope at Support A, put x=0 in slope eq., we get Slope at Support B, put x=L Maximum deflection, is about centre put x=L/2 in Deflection eq., we get
Strength of Materials

17. Numerical:1
Strength of Materials

18. Workout Example : 1
A simply supported beam of span L, carries a point load W at L/4from each support. Find slope at support and maximum deflection.
Draw diagram
Follow Macaulays Method, as per previous derivations.
Ans:
Strength of Materials