# Unit 1: Strength of Materials

Mass (M) is the amount of matter contained in a given body (object). It does not vary with the change in its position on the earth’s surface (latitude & altitude (elevation)).The mass of a body is measured using a lever balance (Physical Balance) by comparing with a standard mass.

Example

Moving an object made of Wood & another object made of Solid Steel, both of same physical size (same volume), in Space. To start moving wooden object will be easy, since mass of wood is less. To start moving steel object will be harder, since mass of steel is more

Weight (W): It is the amount of pull, which the earth exerts upon a given body. (The force of attraction caused by gravitational pull of the earth).

Since the pull varies with the distance of the body from the centre of the earth, the weight of the body will vary with its position on the earth’s surface (latitude and  altitude (elevation)).

Hence Weight is a FORCE that acts on a body or object and is directed toward the center of the earth.

The weight of a body is measured by a Spring Balance (Spring Gauge). The pointer of the spring gauge indicates the varying tension in the spring as the body is moved from place to place.

Example Your Weight. It is the force (your weight) directed along a line of action through you and the centre of the earth (the centre of mass of earth)

Weight (W) (in newtons N) of a body of Mass (M) (in kg) at a place where Gravitational Acceleration is (A)  (in m/s2 ) is given by

W =  M x A     (kg-m/s2     newtons    N)

Force – Force is an action applied to an object which would cause the object to move or change the way it is currently moving or change its shape.

A force can be a push (compressive force) or a pull (tensile force) acting on an object.

Example:

(i) Pushing or Pulling a desk to move it.

(ii) Exerting a force on a foot ball to prevent it from going into the goal.

Force (F) = Mass (M) x Acceleration due to gravity (A) = kg-m/s2

Unit of Force ‘F’= newtons (N)

Load: It is the entire collection of forces acting on the object.

• Force Vector – A force vector is a graphical representation of a force.   Force vectors are drawn as arrows. It shows the direction of the force  and its point of application and magnitude of Force.The direction of the force determines the direction in which the object moves or, if the object is static, the direction in which a counter-force is acting.An Object can be subjected to 5 fundamental forces:(i)  Tensile force

(ii) Compressive force

(iii) Bending force

(iv) Shear force

(v) Torsional force

Tension (Tensile) force is the type of force in which the two sections of material, on either side of a plane, tend to be pulled apart or elongated.

Compressive force is the reverse of tensile force and involves pressing the material together

Bending force involves applying a force in a manner that causes a material to curve and results in compressing the material on one side and stretching (tensioning) it on the other

Shear force involves applying a force parallel to a plane which causes the material on one side of the plane to slide across the material on the other side of the plane

(v)Torsional force is the application of a force that causes twisting in a material

Stress is the force applied to a certain cross-sectional area of an object.

Stress in a bar, which is axially loaded with a force (/stretched in tension) is equal to the applied force divided by the cross-sectional area

Linear-Elastic Region of the Curve – It is part of stress vs strain  curve, where Stress and Strain increases linearly.

i.e., when the stress is reduced, the material will return to its original shape.

#### b) Hook’s Law – In the Linear-Elastic region of the Stress vs Strain curve, Ratio of Stress to Strain is a constant.

1. c) Modulus of Elasticityor Young’s Modulus of a material:

It is the Slope of the Line (y/x), in the Linear-Elastic region of the Stress vs Strain curve.    Unit is pascal (N/m2)

• Young’s Modulus is used to find out how much a rod or wire stretches under a tensile load.
1. d) Yield Strength Point: It is the point at which the Stress-Strain curve deviates from the straight-line relationship and Hook’s Law no longer applies.

From this point onwards some permanent (plastic) deformation occurs in the specimen.