1. Coplanar concurrent Forces

2. Preapred by :
Aghara Navneet
Amrutiya Hasmukh
Korat Dharmesh

3. Mechanics of solids ( )

4. VECTOR ADDITION --PARALLELOGRAM LAW
Triangle method (always ‘tip to tail’):
How do you subtract a vector?
How can you add more than two concurrent vectors graphically ?
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

5. Resultant of Two Forces
force: action of one body on another; characterized by its point of application, magnitude, line of action, and sense.
Experimental evidence shows that the combined effect of two forces may be represented by a single resultant force.
The resultant is equivalent to the diagonal of a parallelogram which contains the two forces in adjacent legs.
Force is a vector quantity.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

6. Addition of Vectors Trapezoid rule for vector addition
Triangle rule for vector addition B C
Law of cosines,
Law of sines,
Vector addition is commutative,
Vector subtraction
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

7. Example
Trigonometric solution - use the triangle rule for vector addition in conjunction with the law of cosines and law of sines to find the resultant.
The two forces act on a bolt at A. Determine their resultant.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

8. Trigonometric solution - Apply the
triangle rule. From the Law of Cosines,
From the Law of Sines,
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

9. RESOLUTION OF A VECTOR
“Resolution” of a vector is breaking up a vector into components. It is kind of like using the parallelogram law in reverse.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

10. CARTESIAN VECTOR NOTATION
We ‘resolve’ vectors into components using the x and y axes system.
Each component of the vector is shown as a magnitude and a direction.
The directions are based on the x and y axes. We use the “unit vectors” i and j to designate the x and y axes.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

11. F = Fx i + Fy j or F = F'x i + F'y j
For example,
F = Fx i + Fy j or F = F'x i + F'y j
The x and y axes are always perpendicular to each other. Together,they can be directed at any inclination.
Statics:The Next Generation (2nd Ed.) Mehta, Danielson, & Berg Lecture Notes for Sections 2.1,2.2,2.4

12. Stress and strain Torsion
Introduction to stress and strain, stress strain diagram
Elasticity and plasticity and Hooke’s law
Shear Stress and Shear strain
Load and stress limit
Axial force and deflection of body
Torsion
Introduction, round bar torsion, non-uniform torsion.
Relation between Young’s Modulus E,  and G
Power transmission on round bar

13. hear Force and bending moment
Introduction, types of beam and load
Shear force and bending moment
Relation between load, shear force and bending moment
Bending Stress
Introduction, Simple bending theory
Area of 2nd moment, parallel axis theorem
Deflection of composite beam

14. Non Simetric Bending Shear Stress in beam Deflection of Beam
Introduction, non-simetric bending
Product of 2nd moment area, determination of stress
Shear Stress in beam
Introduction, Stream of shear force
Shear stress and shear strain in edge beam
Deflection of Beam
Introduction
Equation of elastic curve, slope equation and integral deflection
Statically indeterminate Beams and shaft

15. EQUILIBRIUM OF CONCURRENT COPLANAR FORCE SYSTEMS
Definition:-
If a system of forces acting on a body, keeps the body in a state of rest or
in a state of uniform motion along a straightline, then the system of forces
is said to be in equilibrium.   
ALTERNATIVELY, if the resultant of the force system is zero, then,
the force system is said to be in equilibrium.

16. Conditions for Equilibrium of Concurrent Coplanar Force System
A coplanar concurrent force system will be in equilibrium
if it satisfies the following two conditions:
i)  Fx = 0; and ii)  Fy = 0
i.e. Algebraic sum of components of all the forces of the system,
along two mutually perpendicular directions, is ZERO. Y X

17. Graphical conditions for Equilibrium
Triangle Law: If three forces are in equilibrium, then, they form a closed
triangle when represented in a Tip to Tail arrangement, as shown in Fig 1.(a). F3 F2 F2 F1
Fig 1.(a) F3 F1
Polygonal Law: If more than three forces are in equilibrium, then, they form a closed polygon when represented in a Tip to Tail arrangement, as shown in Fig 1.(b). F4 F3 F3 F2 F5 F1 F2 F4 F1
Fig 1.(b) F5

18. LAMI’S THEOREM
If a system of Three forces is in equilibrium, then, each force of the system is proportional to sine of the angle between the other two forces (and constant of proportionality is the same for all the forces). Thus, with reference to Fig(2), we have,
Note: While using Lami’s theorem, all the three forces should be either directed away or all directed towards the point of concurrence. F3 α F2 F1
Fig (2)

19. Thank you…