 Part One: Material Properties  Part Two: Forces and Torque  Assessment

 1) A Structural Engineering Achievement, eg Sydney Harbour Bridge Eiffel Tower Burj Khalifa Three Gorges Dam  2) A Structural Engineering Failure, eg Tacoma Narrows Bridge I-35W Mississippi River bridge St. Francis Dam Hyatt Regency Walkway

 This topic is all about learning what happens to different materials when we apply forces to them.

 Once we know this, we start to have enough information to plan how to build bridges, buildings, roads, and a multitude of different structures

 Consider a cube of plasticine. What forces could you apply to it to attempt to change its shape?  Tension (Pull)  Compression (Push)  Shear  Torsion  Bend

 If you are having trouble figuring out what is in compression, and what is in tension, do the following thought experiment:  Replace one of the materials with a piece of string. Will the structure still hold up? If so, then that material was in tension

 Q 11 Pg 32  Q 7 pg 37, and Q 11 pg 39

 A girl stands on a wooden bridge, and it bends downwards. Which part of the bridge is in compression, and which part is in tension?

 Some materials are strong in compression, and weak in tension, and vice versa.  Concrete is strong in compression, but weak in tension. We can add steel reinforcing rods, because steel rods are strong in tension.

 Sample Q 10 Pg 26  Q 12 Pg 33  Q 10 Pg 38

 When we test materials, we have two main concepts we need to measure: Stress and Strain  To do this we get the material (eg a steel girder), clamp it into a machine that can either apply a compression or tensile force and measure the how much it compresses/extends with each force.

 Question 4.  Calculate the stress being applied to a steel girder if it has a cross sectional area of 0.02m 2, and a force applied of 5000N  Question 5.  Calculate the stress being applied to a steel girder if it has a cross sectional area of 0.05m 2, and a force applied of 40kN  Question 6.  Calculate the cross sectional area of an aluminium bar than has a 20kN force applied, and is subjected to a stress of 2M Nm -2

 Question 7.  Calculate the strain if a steel girder, originally 10m long, is compressed by 2cm  Question 8.  Calculate the strain if a carbon fibre material, originally 10cm is stretched to a new length of cm  Question 9.  A steel girder is found to have a tensile strain of ε = If its original length was 1m, what is its new length?

 The results of our testing of the material  Draw on board

 Usually two distinct regions:  Elastic Region (straight line)  Plastic Region (not straight)  Any material compressed or stretched less than the elastic limit, will go back to its original shape after the force is removed.  Any material that enters the plastic zone will have permanent deformations.

 The strength of a material is the stress that will cause it to break or fail completely.

 Brittle materials have a very small plastic region (suddenly they just break!)  Ductile materials have a large plastic region (can stretch and stretch, and stay stretched out)

 Question 10  Calculate Young’s Modulus for a human bone that shows a strain of when placed under a stress of 7M Pa  Question 11  Calculate Young’s Modulus for a marble column, that is 2m long, cross sectional area of 0.5m 2, and under a force of 5x10 7 N undergoes a compression of 4mm

 Young’s Modulus of Snakes

 Sample. Q 1, 2, 4, 5, 6.  Q 2, 3, 4, 5.

Extension ( Δx) [m] Force ( F) [N]

 Similarly the area under a stress-strain graph is called the strain energy What is the area under this graph? 100 Strain Stress [MPa]

100 Stress [MPa] Strain A B

Basically F x d = Work Unit: J Area x length = Volume Unit: m 3 Strain Energy Units: Jm -3

 The strain energy needed to break a material gives us a measure of its toughness.

 Sample. Q 3, 7  Q 6, 7  Q 1, 2, 3, 4, 5, 6.

For each question 1. Draw the situation 2. Answer the question 3. Build the contraption to test your answer.

 Which line has the most tension? Or are they the same?

 Which rope has the most tension? Or are they the same?

 The ropes holding the monkey have the same force. Are they bigger, smaller, or same than in the last question?

 Train in middle, but pillars not centred. Is the normal force provided by both pillars the same? If not, which is bigger?

 Try undoing a nut and bolt with your bare hands  Why is it easier to use a spanner?  Try hold the spanner close to the nut, is it easier or harder to undo?  What if you were to apply a force outwards (pull on the spanner)

Force r Axis of rotation

Force r Axis of rotation θ

 Question 12  Calculate the torque when a 10N force is applied at the end of a 10cm spanner 10N 10cm

 Question 13  Calculate the torque applied to a 10cm spanner, when the force is 10N, but is applied halfway along, and at a 30 o angle 10N 5cm 30 o

 Question 14  If an 8N force applied to a wrench produces a 1.6Nm torque, what distance is the force applied from the axis of rotation?

A structure is in static equilibrium (not moving) if TWO conditions are met: 1. Sum of all forces acting on it are zero (Newton’s First Law) 2. Sum of clockwise torques (moments) equals some of anticlockwise torques (moments)

 A bridge is being build out of a 10m, 1000kg slab of concrete, resting on two pillars.  If the left pillar provides a normal force of 5000N, how much does the other provide? 2m 10m

 Same 1000kg bridge, but it is to be built so that one pillar is at the end  What is the normal force provided by EACH pillar now? 10m 2m

 Two hints:  1) The weight force of the bridge can be considered as acting from a single point.  2) Is the bridge rotating? No! So the axis of rotation can be chosen to be anywhere! 10m 2m

 A cantilever is essentially a diving board.  It is a structure where it needs an upwards and downwards normal force  How could we make the following structure steady? Water

 Q 8, 9  Q 9

 Struts and ties can help distribute a load or reduce the load in a beam or a column.

 Sample. Q 8, 9  Q 7, 8

 An arch is a useful building structure as it supports the weight above it using only compression forces.