CHAPTER 1 (b)

FORCES ON MATERIAL

Learning OutcomeAt the end of this lecture, student should be able to;Understand Hookes LawDefine modulus of elasticity or Young ModulusUnderstand stress strain curveDefine strain energy, factor of safety, Poissons ratio, modulus of rigidityUnderstand tensile test Define shear stress (single and double)Solve problems related to above learning outcomes

What is Hookes Law?Hookes Law states that , the elongation (strain) is proportional to the force (stress) at any elastic material as long as the elastic limit is not exceeded.The material returns to its original shape and size after the force is removed.

The Hookes law can be defined as,

Or

The constant, E in Hookes Law is knows as modulus of elasticity or Young Modulus.Young modulus is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. (The higher E value, the higher its strength)Unit is in N/m2 @ Pa.

Young Modulus Value of Several Engineering Material

MaterialYoung Modulus, E (GPa)Steel200 - 220Aluminum60 - 80Copper90 - 110Bronze100 - 125Wood10

Tensile TestTensile test test in which sample is subjected to tension force until failure. The results from the test are commonly used to select a material for an application, for quality control and to predict how a material will react under tensional forces. Properties that can be measured - ultimate tensile strength, maximum elongation, reduction in area, yield strength, young modulus and strain hardening characteristics. (movie)

Necking Phenomenon

Tensile Test Resulta) Graph Gradient (obtained from graph)

b) Young Modulus

Tensile Test Result

Stress-Strain Curve

Stress-Strain Curve Explanation

a) Proportional Limit- Stress is proportional to strain (Hookes Law ) which indicated by a straight line.

b) Elastic Zone- The specimen will regain its original shape and size when the load is removed.

c) Plastic Zone- Opposite to elastic zone, where the specimen cant regain its original shape and size when the load is removed. Any deformation after this zone is said to experience strain hardening.

Ultimate tensile strengthNeckingBreaking pointProportional limitYield point

d) Yield Point- Point at which permanent deformation of specimen begins to take place. This is a point on the stress-strain curve at which the Hookes Law is no longer obeyed @ proportional limit is off.

e) Ultimate stress / ultimate strength- The maximum stress that a specimen can withstand while being pulled.

f) Breaking Point- After the specimen reach the ultimate stress, a necking phenomenon is formed where the cross-sectional area of specimen decreased. Further stress will result in failure/rupture to the specimen.

Strain-Stress Graph(Comparison with different material)

Strain EnergyWork that must be done to produce a strain.Unit in Nm or Joule (J) or V = AL

Where;U = strain energyP = load / forceL = original lengthA = cross sectional areaE = Young Modulus

Poissons RatioWhen a material is stretched, its cross-sectional area changes as well as it length in the direction of stretching force.

- X axis, x = Y axis, y =

Poissons ratio can be expressed as;

Where; = poissons ratio , no unity = tranverse or lateral strainx = longitudinal or axial strain Poissons ratio has NO unit.

Factor of Safety

Also known as safety factor is the ratio between ultimate tensile stress to the working stress.SF has No unit.

Where;

SF Safety factoru - Ultimate stressw - Working stress

Modulus of Rigidity

The ratio between shear stress to the shear strain.It is denoted by G, C or N.Unit in N/m2 or Pa

or

Shear StressRatio between shear load to the shear area.Unit in N/m2 or Pa.

or

ExerciseA round bar of mild steel 5.4 m long and 38 mm diameter is lengthened by 1.66 mm under a load of 70 KN. Find the strain, stress and Young modulus.A bar of 30 mm diameter is subjected to a force of 58.8 KN. The measured extension on a gauge length of 200 mm is 0.09 mm and the change in diameter is 0.0029 mm. Calculate the Poissons ratio. A bar with a length of 100 mm and diameter of 10 mm is applied to 50 KN load. Calculate the strain energy. (Given E= 70 GPa)4. A steel with a diameter 20 mm is subjected to tensile force of 100 KN. Find the factor of safety if the ultimate stress is 200 MPa.

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