JJ310 STRENGTH OF MATERIALS

JJ310 STRENGTH OF MATERIALS1FORCES ON MATERIALS - Understand the forces on materialsA aread diameterd change in diameterE Youngs modulusF or P ForceG Modulus of rigidityL lengthU strain energy

L change in length - strain - shear strain - density - stress - shear stress - poissons ratioBASIC SYMBOL USING IN STRENGTH OF MATERIALS:-2The Types Of Loads And Their EffectThe type of force on materials:-a. static b. dynamic c. impact d. fatigue and alternating loads Static force- do not change- example:- the building

3Impact Force In mechanics, an impact is a high force or shock applied over a short time period when two or more bodies collide.Example: During the hammer touches the nail

Dynamic force- constantly changing- example:- the vehicle on the bridge

Fatigue and alternating loads- Charges in effect at certain times. - example:- i. the shaft is mounted on the windmill. ii. when a load is suspended on a spring.

5The effect of force on materials:-

It become to resulted in extension

It become to resulted in shorten

It become to resulted in bending

It become to resulted in shearing

It become to resulted in torque6The effect of force on materials:-

resulted in extensionBeforeAfterLOAD7

resulted in shortenBeforeAfter8

resulted in bending9

resulted in shearing10

resulted in torqueTorsion11Tensile stressFigure above shows a bar on forces P. The force P applied will cause the bar having extension.

Bar subjected to the force PA, area12If the observed cross-section of the shaft, we find there is force be acting on a cross section x-x of the plane. To ensure it is in a situation of equilibrium, a force opposite value P must be produced.

This internal force is called STRESS, and it is a response to external forces for load P.

Internal Force at XX- section13Type of stressThere are three types of stress;-

a. Tensile stress.

b. Compressive stresses.

c. Shear stress.

Stress depends on the magnitude and direction of force applied and the cross-sectional area of the stress () is the ratio of force (P) with a cross-sectional area (A).

14The average unit stress, here after call stress (), is a measure of the intensity of the applied and resisting force.The stress is often determined by dividing the total applied load (F) by the total area resisting deformation by the load (A);

The unit of stress are Newtons per square meter (N/m2 ). One Newton per square meter is equal to a Pascal (Pa).

15The average amount of distortion per unit length is called the unit strain hereafter called strain ().The strain is often determined by dividing the total change in length of sample (L) by the original length (L);

Strain has no net unit since it is defined as the meters of change per meter of length (m/m). The units always cancel. Consequently any units may be attached to the number representing strain.

16Tensile StressTensile stress occurs when a material is subjected to pulling or stretching force. Stress is defined as a force applied over a cross-sectional area, with typical units of pounds per square inch (psi) or Newton per square meter, also known as Pascal (Pa).

The type of stress that a material is exposed to will depend on how the force is being applied. The three basic types of stress are tensile, compressive, and shear. An understanding of tensile stress is important in selecting materials for mechanical engineering and design applications.

17Tensile StressThe dimensions of an object under stress will change due to the strain or deformation that occurs when a force is applied. A material that is under tensile stress will elongate, or stretch, when it experiences strain.

A material exposed to low stress will return to its original dimensions after the force is removed. At high stresses, a material may not return to its original state when the force is removed and permanent deformation will occur. The relationship between the applied stress and the corresponding strain can be used to predict the behavior of a material when it is exposed to tensile stress.

18Compressive StressCompressive stress is the capacity of a material or structure to withstand axially directed pushing forces. When the limit of compressive strength is reached, materials are crushedCompressive strength is often measured on a universal testing machine. Measurements of compressive strength are affected by the specific test method and conditions of measurement. Compressive strengths are usually reported in relationship to a specific technical standard that may, or may not, relate to end-use performance.

19Tensile strainTensile strain represents the amount of stretch produced, divided by the original length of the test piece.

The dimensions of an object under stress will change due to the strain or deformation that occurs when a force is applied. A material that is under tensile stress will elongate, or stretch, when it experiences strain. A material exposed to low stress will return to its original dimensions after the force is removed.

20Youngs ModulusIn solid mechanics, the slope of the stress-strain curve at any point is called the tangent modulus. The tangent modulus of the initial, linear portion of a stress-strain curve is called Young's modulus, also known as the tensile modulus. It is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. It is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It can be experimentally determined from the slope of a stress-strain curve created during tensile tests conducted on a sample of the material. In anisotropic materials, Young's modulus may have different values depending on the direction of the applied force with respect to the material's structure.

21Youngs Modulus22ExerciseA 2.5 m rod with cross sectional area of 1290 mm2 extends by 1.5 mm when applied with a tensile force of 140 kN at both ends.Draw a free body diagram for the above situation.Calculate the tensile stress in the rod. Determine the strain. Determine the Youngs Modulus of the rod.23ExerciseA 4 meter long copper wire is loaded with a load of 100 kN. If the stress in the wire is 60 MN/m2, calculate the:-i. strain of the wire ii. elongation of the wire

Given Ecopper = 112 GN/m2 24