1 STRESS There are 4 main types of stress: Tension Compression Bending Torsion Tension When an object is being stretched it is said to be under tension, e.g. in a tug- o-war the rope is said to be in tension. A member under tension is called a TIE. Definition – “the amount of force being applied per unit area” Units – N/m 2 or Pascals TIE Compression When an object is being crushed it is said to be in compression, e.g. house bricks. A member in compression is called a STRUT. STRUT

2 Bending If an object is being bent, e.g. a bending moment is present, it is said to be experiencing bending stress, e.g. when a diver is stood on a diving board, the diving board experiences a bending stress. Torsion Another word for torsion is “twisting”, if you take hold of a tube and turn one end clockwise, and the other end anti-clockwise, the tube would be experiencing a torsional stress. Type of stressFormula Tension F/A Compression F/A Bending MY/I Torsion Grθ/L FORMULAE Note: Other formulas do exist, however we do not need to worry about them for this unit.

3 Definition of terms F – Applied force, measured in Newtons A – Cross sectional area M – Bending moment y – Distance from neutral axis to max point of stress Neutral axis

4 I – Second moment of area or moment of Inertia. This tells us how resistive to bending a cross section is. The formula for second moment of area for a rectangular section is bd 3 /12 XX Y Y b d The above diagram assumes that we are bending about the X axis, if we were to bend about the Y axis, the b and d terms would be the other way round. G – Shear modulus. This is a material property, each material will have its own specific shear modulus (see material property tables). θ – Angle of twist (radians) L – Length of the object being twisted.

5 Stress – Problems For all of the problems given below, assume that everything is made from Titanium 6Al-4V 1. A titanium bar of radius 20mm undergoes a tensile force of 10KPa. a)Calculate the stress in the bar b)Will the bar fail in tension? 2. Calculate the maximum bending stress in the beam shown below 5KN 2m 0.2m 0.01m Cross section