Engineering mechanics

ENGINEERING MECHANICS

While scientists are keen on understanding and establishing the Laws of Mechanics, we, the engineers, are interested in applying these laws to the actual field problems. Application of the Laws of Mechanics to the actual problems is termed as Engineering Mechanics or Applied Mechanics.

Leonardo da Vinci (1458–1519) wrote: “Mechanics is the paradise of mathematical science, because here we harvest the fruits of mathematics.” The three fundamental areas of engineering mechanics are: Statics, Dynamics and Strength of Materials of rigid bodies. Rigid bodies are bodies for which the change in shape due to the loads can be neglected.

Statics: Statics concerns the study of the external effects of forces acting on rigid bodies, which are in a state of equilibrium.

Dynamics: Dynamics concerns the study of the external effects of forces acting on rigid bodies, which are in motion.

Strength of Materials: Strength of Materials deals with the study of internal effects on the bodies due to externally applied loads.

Basic concepts of Stress, Strain and the three Moduli of Elasticity, viz., Young's Modulus, Rigidity Modulus and Shear Modulus, forming part of the area of strength of materials, are discussed in this chapter.

 

1. UNITS

A Unit represents the dimension of a physical quantity. A unit is defined as a numerical standard used to express the qualitative measure of a physical quantity. Mechanics deals with four fundamental quantities: (i) Length, (ii) Mass, (iii) Force and (iv) Time.

Different Systems of Units

Different systems of units are: (1) C.G.S. Units, (2) M.K.S. Units and (3) S.I. Units

(1) C.G.S. Units: In C.G.S. System, centimeter, gram and second are the units of length, mass and time respectively.

(2) M.K.S. Units: In M.K.S. System, meter, kilogram and second are the units of length, mass and time respectively.

(3) S.I. Units: S.I. is the internationally adopted abbreviation of the Système International d' Unités. It means International System of Units. S.I. Units are adopted all over the world since 1960.

In S.I. Units, there are three classes of units, viz., (i) Base Units, (ii) Supplementary Units and (iii) Derived Units.

(i) S.I. Base Units

Quantity | Name of Unit | Symbol

Length     :   meter        :    m

Mass       :  kilogram     :   kg

Force      :  Newton      :   N

Time      :  second        :   s

(ii) S.I. Supplementary Units

Units of plane angle and solid angle are said to be supplementary units. Radian is unit of plane angle. Its symbol is rad. Steradian is the unit of solid angle. Its symbol is sr.

(iii) S.I. Derived Units

Most of the units used in physical sciences and engineering mechanics are derived from the base and supplementary units.

Examples:

Volume = Length × Breadth × Depth = m³

Density = Mass/Volume = kg/m³

Linear Velocity = Distance covered/ Time = m/s

 

S.I. Units used in Mechanics

Units other than S.I. Units

 

2. EXTERNAL FORCES

Force: Newton's First Law of Motion provides the basis for the definition of force. The Second Law provides the basis for the definition of the magnitude of force. External Force (P): External Force is the force acting on a body due to external causes. The external forces constitute the load on a structure. The load (external force) acting on a structure tends to cause deformation in the structure. The unit of load (force) is Newton (N).

Mechanical Properties of Materials: A design engineer should know the mechanical strength properties of various materials for determining the dimensions of the structural elements. If he/she has to select the material or to use a given material, he/she should get satisfied that the material to be selected or given has the required strength properties. For this, one has to resort to tests on strengths of building materials in the laboratory. The tests include tension test, compression test, etc.

Classification of External Forces or Loads acting on a Structure

The loads acting on a structure are External Loads. These loads are classified as follows:

(i) According to the manner of application as Static Loads and Dynamic Loads

Static loads are loads applied gradually from zero. No vibration is produced. Equilibrium of the structure exists.

Dynamic loads are loads applied rapidly. They vary with time. Dynamic loads cause vibration. Equilibrium of the structure does not exist. However, natural damping forces cause the damping and ceasing of the vibration.

(ii) According to the Area of Distribution as Uniformly Distributed Loads and Concentrated Loads

Distributed loads are loads spread over a larger area or along the length of a structural member. The distribution of load may be uniform or non-uniform also. Examples: (i) Self-weight of a beam slab acting on a wall along its length. (ii) Water load acting on the upstream side of the dam structure.

Concentrated loads are also known as Point Loads. Point Loads, as such, do not exist in practical cases. Point load is applied when the load acts on a relatively smaller area compared to the overall structure. Example: Load transferred by a column on its foundation.

(iii) According to the Duration of Loading as Dead Loads or Live Loads

Dead loads are loads which remain constant for a long time.

Examples: Self-weight of the various components of a building structure. Live loads are loads applied on a structure for a short time. They change their magnitude and direction with time.

Examples: (i) Vehicular traffic on a bridge, (ii) Weight of persons and weight of materials stored temporarily in a floor.

Note: The self-weight of a beam is a static load, dead load and distributed load. The wheel load of a truck moving over a bridge is a dynamic load, a live load and a concentrated load.

 

3. INTERNAL FORCES

Deformation due to External Loads: When a body or a material is subjected to external loads or forces, it undergoes a deformation. Deformation means change in dimension or change in shape or both simultaneously. Under a direct pull, the body elongates; under a direct push it contracts; under transverse loads it bends; under torsion it twists.

Internal Resistance: During deformation, the material offers a resistance against deformation, by virtue of its strength and stiffness. That is, this deformation is opposed or resisted by the intermolecular forces developed within the material of the body.

Equilibrium: The internal resistance developed within the material increases as the deformation increases. When the internal resistance becomes is equal to the external loads, the deformation stops. Equilibrium condition exists now. If the internal resistance induced is less than the external loads, the deformation continues till the material fails, i.e., breaks.