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

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

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

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

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

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

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

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

SSB with Point Loads Slope Equation Deflection Equation Strength of Materials

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

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

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

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

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

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

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

Numerical:1 Strength of Materials

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