Engineering Mechanics: Lami's Theorem and Cylinder Reactions Problem

This course material covers Lami's Theorem in Engineering Mechanics taught by Ranbir Mukhya. It includes an outline of the theorem, problem scenarios involving cylinders with given weights and diameters, and the determination of reactions at various points. Detailed force diagrams and calculations are provided to demonstrate solving for reactions using the principles of equilibrium and Lami's Theorem.

• Engineering
• Mechanics
• Lamis Theorem
• Cylinder Reactions
• Problem Solving

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1. Engineering Mechanics Lami s Theorem Course Faculty Name Ranbir Mukhya

2. Outline Lami s Theorem: If F1 + F2 + F3 = 0 F2 F3 Then , F1 Sin ( ) Sin ( ) Sin ( ) = F2 = F3 Where F1 , F2 and F3 are magnitude of the forces. F1

3. Problem 1. Two cylinders of diameter 60 mm and 30 mm. weighing 160 N and 40 N respectively. Assuming all the contact surfaces to be smooth. Find the reactions at A, B and C Diameter = 30 mm Do Your self Diameter = 60 mm

4. Problem FBD : Cylinder-1 FBD : Cylinder-2 RD RA RC RB RD WE WF

5. Problem FBD : Cylinder-1 RD RA 450 450 RB WE 450

6. Problem FBD : Cylinder-1 Q F RD RD Q E RA Cylinder-2 450 RB WE Cylinder-1 EF = radius of cylinder-1 + radius of cylinder-2 = 30 mm + 15 mm = 45 mm Sin( ) = QF EF QF= 72 mm- radius of cylinder-1 radius of cylinder-2 = 72 mm 30 mm 15 mm = 27 mm = 27 / 45 = ??

7. Problem Sin( ) = QF EF FBD : Cylinder-2 = 27 / 45 1. Force equilibrium about x- axis: RD = ?? Summation of force along x axis = 0 RC RD * Sin ( ) - Rc = 0 2. Force equilibrium about y-axis: Summation of force along y-axis = 0 40 N RD * Cos ( ) 40 = 0 RD = ?? RC = ??

8. Problem FBD : Cylinder-1 Sin( ) = QF EF RD = ?? = 27 / 45 = ?? RA 450 RB WE