Stress,strain,load

STRESS, STRAIN & LOAD

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Load A load may be defined as a force tending to effect and

produce deformations, stresses or displacements in the structure.

Common loads in engineering applications are tension and compression

Tension :- Direct pull ex :- Force present in lifting hoist Compression :- Direct push ex :- Force acting on the pillar of a building Sign convention followed: Tensile forces are positive and

compressive negative

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Types of load There are a number of different ways in which load can

be applied to a member. Typical loading types are:

(a) Dead/ Static load(b) Live load(c) Impact load or shock load(d) Cyclic loads & Repeated loading

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Dead Loads

“ Non fluctuating or static forces generally caused by gravity and relatively constant for an extended time.”

Weight of the structure Ex :- Floors, Beams, RoofsLoads that are “always there”

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Dead Loads

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Live Loads “ Load due to dynamic effect. This are usually unstable or moving loads.”

Loads that may move or change mass or weight

ex: People, furniture, equipment Load exerted by a lorry on a bridge

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Live Loads

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Impact loads:

Impact load is caused by vibration or impact or acceleration.

The dynamic effect on a stationary or mobile body as imparted by the short, forcible contact of another moving body.

A mass, with a known velocity, hitting an object and thereby causing a suddenly applied impact load.

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Cyclic load

“A load which is applied over and over.”

Cyclic load on a structure can lead to fatigue damage or failure. These load can be repeated loading on a stricture or can be due to vibration.

For example, if you twist a wire again and again with the same effort, it breaks after a point, though you're applying the same force.

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Strain

When a body is subjected to some external force, there is some change of dimension of the body. The ratio of change of dimension of the body to its original dimension is known as strain.

Strain is a dimensionless quantity.

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Types of strain

a) Tensile strain b) Compressive strain c) Volumetric strain d) Shear strain

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Types Of Strain

Tensile strain :- Ratio of increase in length to original length of the body when it is subjected to a pull force.

Compressive strain :- Ratio of decrease in length to original length of the body when it is subjected to a push force.

Volumetric strain :- Ratio of change of volume of the body to the original volume.

Shear strain :- Strain due to shear stress.

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Stress

When a material is subjected to an external force, a resisting force is set up within the component, this internal resistance force per unit area is called stress.

SI unit is N/m² or Pascals 1kPa=1000Pa, 1MPa=10 Pa, 1 Gpa=10 Pa, ⁶ ⁹ 1 Terra Pascal=10¹² Pa

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Types of stress

1) Normal stress :- It is the stress which acts in direction perpendicular to the area.

Normal stress is further classified into tensile stress and compressive stress.

It consists ;a. Tensile stressb. Compressive stress

2) Shear stress

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Tensile stress

It is the stress induced in a body, when it is subjected to two equal and opposite pulls (tensile forces) as a result of which there is a tendency in increase in length.

It acts normal to the area and pulls on the area.

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Tensile stress

Under tensile stress the bar suffers stretching or elongation

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Tensile stress

Consider a uniform bar of cross sectional area A subjected to an axial tensile force P. The stress at any section x-x normal to the line of action of the tensile force P is specifically called tensile stress . Since internal resistance R at x-x is equal to the applied force P.

Tensile stress=(internal resistance at x-x)/(resisting area at x-x) =R/A =P/A.

Tensile strain (e)=Increase in length/Original length = dL/L

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Compressive stress

Stress induced in a body, when subjected to two equal and opposite pushes as a result of which there is a tendency of decrease in length of the body.

It acts normal to the area and it pushes on the area.

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Compressive stress

Under compressive stress the bar suffers shortening.

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Compressive stress

If the bar is subjected to axial compression instead of axial tension, the stress developed at x-x is specifically called compressive stress.

Compressive stress = R/A = P/A.

Compressive strain= Decrease in length/ Original length = δL/L

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Sign convention for direct stress and strain:-

Tensile stresses and strains are considered positive in sense producing an increase in length.

Compressive stresses and strains are considered negative in sense producing decrease in length

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Shear stress Stress Induced in a body, when subjected to two equal

and opposite forces which are acting tangentially across the resisting section as a result of which the body tends to shear off across that section.

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Shear stress

Consider the section x-x of the rivet forming joint between two plates subjected to a tensile force P as shown in figure.

The stresses set up at the section x-x acts along the surface of the section, that is, along a direction tangential to the section. It is specifically called shear or tangential stress at the section and is denoted by σ. σ = R/A = P/A.

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Elastic module

Hooke’s law states that: “When a body is loaded within elastic limit, the stress is proportional to strain.” or “Within the elastic limit the ratio of stress applied to strain developed is a constant.”

The constant is known as Modulus of elasticity or Elastic modulus or Young’s modulus.

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Elastic module

Mathematically within elastic limit, E = Stress/Strain=σ/e

but, σ= P/A; e =δl/l E=P*l/A*δl

δl=P*l/A*E Young's modulus (E) is generally assumed to be the

same in tension or compression and for most of engineering applications has a high numerical value.

Typically, E=210 x 10⁹ N/m² or E = 210 GPa for steel

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