An Introduction to engineering analysis Why Structures Fail An Introduction to engineering analysis

Building a Tower Each team will design a tower made of balsa sticks Each team will do a structural analysis of their tower to predict where it will fail Each tower will under go ‘destructive testing’

The Language of Engineers Mass Position Velocity Acceleration Force Pressure Stress Deformation System Failure

Mass A measure of how much matter an object is made of Does not change with environment Metric Unit: ? English Unit: Pounds (lb or lbm) Grams (g) Weight: (in pounds force) 200 lbf 90 kg 200 lbm 90 kg 200 lbm Weight: 33 lbf

Position Position fully defines an object’s location in space Metric Unit: Meters (m) English Unit: Feet (ft) (X, Y, Z) = (.2 m, .5 m, .6 m) (X, Y, Z) = (1 m, .3 m, .4 m) Y Z (X, Y, Z) = (.5 m, .1 m, .2 m) X

Velocity Velocity describes the rate of change of an object’s position 30 m/s Metric Unit: Meters per second (m/s) English Unit: Feet per second (ft/s) Includes both a magnitude and direction 30 m/s 10 m/s Can also be expressed as a ‘vector’ (x,y) = (3 m/s, 4 m/s) 4 m/s 3 m/s

Acceleration Acceleration describes the rate of change of an object’s velocity Metric Unit: m/s/s (m/s2) English Unit: ft/s2 V = 10 m/s a = 0 m/s2 V = 10 m/s 0 sec 1 sec 2 sec 3 sec 4 sec 5 sec 0m 10m 20m 30m 40m 50m 0 sec 3 sec 1 sec 2 sec V = 10 m/s V = ? 16 m/s a = 2 m/s2

Force Any influence that causes an object to change speed, direction, or shape Force = mass * acceleration F = m*a m = 90 kg a = 9.81 m/s2 m*a = 883 N Metric Unit: Newton (N) English Unit: Pounds Force (lbf) F = 500 N a = 5 m/s2 100 kg

Pressure P = F / A When a force is exerted over a defined area Pressure = Force / Area P = F / A Force = 500 lbf Metric Unit: Pascals (Pa) English Unit: Pounds per square inch (PSI) 24 inches 24 inches Area = 24 in x 24 in = 576 in2 P = 500 lbs / 576 in2 = .87 PSI

Stress A measure of the internal forces acting on a deformable structure Metric Unit: Pascals (Pa) English Unit: Pounds per square inch (PSI) F = 5000 kg * 9.81 m/s2 = 49050 N F = 883 N 20 m 20 m 20 m * 20 m = 400 m2 Stress = P = 49050 N / 400 m2 = 122 Pascals Stress = P = 883 N / 400 m2 = 2.2 Pascals

Stress Types of stresses Tension Compression Shear

Deformation Occurs when the stress in an object exceeds the yield strength of the material 500 kPa Material: Purple Block Yield Strength: 1000 kPa Stressed 1200 kPa kPa = kilo-pascal Or 1000 pascals Deformation!

System Failure Occurs when the stress in an object exceeds its ultimate strength (Compressive or Tensile) 500 PSI Material: Purple Block Yield Strength: 1000 PSI Ultimate Strength: 2000 PSI Stressed 1200 PSI Deformation 2500 PSI System Failure!

Tower Failure Boom! Next Week: Where will your tower fail?