GUJARAT TECHNOLOGICAL UNIVERSITY AHMEDABAD

GOVERNMENT ENGINEERING COLLEGE GODHRA

DEPARTMENT OF MECHANICAL ENGINEERING 3RD SEMESTER MECHANICAL MECHANICS OF SOLID (2131003) YEAR-2014

Coplanar Concurrent Forces Chapter 2 Coplanar Concurrent Forces

Introduction - Definition Concurrent Force Systems: A concurrent force system contains forces whose lines-of action meet at some one point. Forces may be tensile (pulling)

Introduction - Definition Concurrent Force Systems: A concurrent force system contains forces whose lines-of action meet at some one point. Forces may be compressive (pushing)

Introduction - Definition Force exerted on a body has two effects: The external effect, which is tendency to change the motion of the body or to develop resisting forces in the body The internal effect, which is the tendency to deform the body.

Introduction - Definition If the force system acting on a body produces no external effect, the forces are said to be in balance and the body experience no change in motion is said to be in equilibrium. The process of reducing a force system to a simpler equivalent stem is called a reduction. The process of expanding a force or a force system into a less simple equivalent system is called a resolution.

Resultant of Concurrent Force (Algebraically) Find ∑ Fx, ∑ Fy then determine the resultant force and the angle. (The sense in which each force acts is considered) Ax = A cos α, Bx = B cos β, Cx = C cos γ Ay = A sin α, By = B sin β, Cy = C sin γ ∑ Fx = A cos α - B cos β - C cos γ ∑ Fy = A sin α - B sin β - C sin γ Resultant force, R = [(∑ Fx)2 + (∑ Fy)2]1/2 Direction or angle, tanθ′ = ∑ Fy / ∑ Fx

Introduction - Definition A force is a vector quantity that, when applied to some rigid body, has a tendency to produce translation (movement in a straight line) or translation and rotation of body. When problems are given, a force may also be referred to as a load or weight. Characteristics of force are the magnitude, direction(orientation) and point of application.

Equilibrium A system of forces where the resultant is zero is said to be in Equilibrium. (Defined by Newton’s First Law) Now If, R= 0 then, ∑ Fx = 0 ∑ Fy = 0 The above two equations can be used to find two unknowns.

Introduction - Definition Scalar Quantity has magnitude only (not direction) and can be indicated by a point on a scale. Examples are temperature, mass, time and dollars. Vector Quantities have magnitude and direction. Examples are wind velocity, distance between to points on a map and forces.

Introduction - Definition Collinear : If several forces lie along the same line-of –action, they are said to be collinear. Coplanar When all forces acting on a body are in the same plane, the forces are coplanar.

Introduction - Definition Type of Vectors Free Vector - is vector which may be freely moved creating couples in space. Sliding Vector - forces action on a rigid body are represented by vectors which may move or slid along their line of action. Bound Vector or Fixed Vector - can not be moved without modifying the conditions of the problem.

Introduction - Definition Principle of Transmissibility The principle of transmissibility states that the condition of equilibrium or of motion of a rigid body will remain unchanged if a force F action at a given point of the rigid body is replace by a force F’ of the same magnitude and the same direction, but acting at a different point, provided that the two forces have the same line of action.

Introduction - Definition Principle of Transmissibility Line of action

Free Body Most bodies in equilibrium are at rest. But a rigid body moving with constant speed in a straight path is also in equilibrium. A rigid body may be any particular mass whose shape remains unchanged while it is being analyzed for the effect of forces. Since no body is truly rigid, we mean by ‘rigid body’ is one whose deformation under force is negligible for the purposes of the problem. A free body is a representation of an object, usually a rigid body , which shows all the forces acting on it. (See page 22-23 of Analytic Mechanics by Virgil Moring Faires for details)

Introduction - Definitions Types of Forces(Loads) Point loads - concentrated forces exerted at point or location Distributed loads - a force applied along a length or over an area. The distribution can be uniform or non-uniform.

Introduction - Definitions Resultant Forces If two forces P and Q acting on a particle A may be replaced by a single force R, which has the same effect on the particle.

Introduction - Definitions Resultant Forces This force is called the resultant of the forces P and Q and may be obtained by constructing a parallelogram, using P and Q as two sides of the parallelogram. The diagonal that pass through A represents the resultant.

Introduction - Definitions Resultant Forces This is known as the parallelogram law for the addition of two forces. This law is based on experimental evidence,; it can not be proved or derived mathematically.

Introduction - Definitions Resultant Forces For multiple forces action on a point, the forces can be broken into the components of x and y.

Trusses: Joint to joint method A determinate structure is one wherein the internal forces in the various members of the structure may be obtained by the conditions of equilibrium. Although truss is subjected to all manner of loading, for simplicity it is assumed that, the loads on truss are applied at pin joints So, with a truss loaded in this manner, all the various members are two force members and the free body of each pin is a system of concurrent forces. If all the external forces including the reactions at the supports are known, then the above principles can be used to determine the internal forces in each member. To determine the member forces, it is assumed that the unknown forces are acting away from the pin, which means that the members are in tension. Solve for each of the unknowns by using the conditions of equilibrium, i.e., ∑ Fx = 0, ∑ Fy = 0.

130600119006: BILWAL VIJAY 130600119009: CHAUHAN VISHAL K. PREPARED BY : 130600119006: BILWAL VIJAY 130600119009: CHAUHAN VISHAL K. 130600119010: DABHI ANKIT