ENG H192: Hands on LabsLab 4: Stress and StrainEngineering Disciplines Explored: MechanicalIntroductionBackgroundPurposeBasicPrinciplesLabExperienceStress and strain are important mechanical engineering and materialsscience engineering concepts. Materials are often chosen for applicationsbased on their response to applied force (stress). Strain is a unit-lessmeasure of the temporary deformation such stresses can cause. Whenconstructing a building, the materials must be able to withstand the forceof wind and weather conditions, along with the weight of the wholestructure. Submarines must be able to withstand the stress of a greaterpressure when deep under sea without experiencing much deformation.Soda can tops need to bend easily when a force is applied to them. Inevery materials choice, there is the need to determine what properties aremost important, and stress and strain that the material can undergo beforepermanent deformation are two common factors in these decisions.This lab will provide methods to analyze stress and strain in two differentways. The purpose of the static portion of the lab is to find a correlationbetween the weight of the bicycle rider and the stress/strain due to loadingof the front fork. The dynamic portion of the lab will observe the resultsof changing forces on the bike. This will involve measuring the loadingconditions in the front fork of a bicycle while being ridden over obstacles,and to compute the maximum and minimum stress values.This lab write-up will discuss some of the basic principles behind:1. Stress and strain1. Hooke’s Law1. Transducers1. Wheatstone BridgesThis lab write-up will cover the basic principles behind:1. Static Test using a bicycle rider on stand still1. Dynamic Test with various loading conditions with a bicyclerider while the bike is being ridden.FundamentalsStress andStrainUsingHooke’sLawStress and Strain are linearly related to each other by Hooke’s law. Stressis a force applied over an area, while strain is a measure of thedeformation the material experiences, as a fraction of its original shape.Strain: e = Dl lFor example, if an applied stress causes a 10 cm long material to extend inonly 1 direction, and that extension increases the length to 12 cm, then thestrain is .2. Notice that strain has no units. Young’s Modulus is astiffness constant that relates stress and strain, and is a property of thematerial. Young’s modulus has units (psi used in this lab) which areequivalent to the units of stress. Thus, strain can be a unit-less quantity.As stress increases on an object, the strain increases also. Most materialshave a linear region called the elastic region. In this region, if stress isapplied, the material will undergo a deformation (strain) but when thestress is removed, the material will go back to its original shape. This canbe modeled using Young’s modulus. As stress increases, the materialenters a plastic region, which means that the material will deform and nolonger return to its original shape completely when stress is removed.Hooke’s law can no longer be applied. Eventually the material will break.Some materials, such as ceramic, break before they even reach the plasticregion.Stress can be calculated in a variety of different ways. If the force beingapplied is known, and the area of the material is known, than stress can becomputed directly. While in a material’s elastic region, using Hooke’slaw, if the strain is known and Young’s modulus is known for thematerial, then stress is the product of the two. Similarly, if any two ofthose quantities are known, the third can be calculated. Applied stress canbe difficult to find using the first method, because in many cases there area number of forces acting on an object. Thus, measuring the strain on anobject becomes the easiest way to determine the stress. This can be doneby personal observation, or electronically, using a transducer to convertthe physical measurement (strain) to an electrical signal.Transducer:StrainGagesWheatstoneBridgeTransducers are used to convert electrical quantities to physical quantitiesor vice versa. A speaker is a transducer because it converts an electricalsignal to a sound wave. Conversely, a thermostat has a transducer in itthat converts the current temperature to an electrical quantity that can becompared with the desired temperature (also modeled as an electricalsignal). Thus, the thermostat can correctly determine when the heatershould be turned on or off. The transducer used in this lab is a strain gage.This gage changes its resistance based on the deformation that it sees inthe material it’s measuring. This change in resistance is converted to avoltage using a Wheatstone bridge.The Wheatstone bridge is named after Sir Charles Wheatstone, who didnot invent it, but did come up with a variety of uses for it. It is anelectrical bridge circuit that uses four resistors, as seen in Figure 1(below). The bridge measures an unknown resistance when three of theresistances are known. The three known resistances are adjusted untilthere is no current passing from S+ to S-. A voltage is then measuredacross here, and sent to an amplifier.Figure 1. Wheatstone BridgeLab ExperienceMake sketches of equipment used in class and include them in your lab write-up..Static TestDynamicTest1. Set up the data logger as described in the Reference Guide a theend of this write-up. Record each rider’s weight.2. Make sure that the initial output signal without a rider is near twovolts. Record the obtained value.3. With the bike trainer attached to the bicycle, collect data with thedata logger for each member of your group. Use the followingsequence to collect one set of data (all times are approximate). Donot stop the data logger between each step or between each rider.• 5 seconds for an unloaded bike• 10 seconds for rider 1 in riding position (no pedaling)• 15 seconds for rider 1 pedaling• Repeat for remaining team members4. Upload your data from the data logger to the PC. Export your dataas an ASCII file (consult the Quick Reference Guide) and save iton a diskette.1. Select the lightest and heaviest person in your team. These two willride the bike.2. Set up the data logger as described in the Quick Reference Guide.Use the “real-time data acquisition” mode to view the datacollected by the data logger.3. Make sure that the initial output signal without a rider is near twovolts.