MaterialsWhy we need to know about materialsElectrical ResistivityThermal ConductivitySpecific Heat (heat capacity)Coefficient of Thermal ExpansionDensityStress and StrainStress and Strain, IllustratedElastic ModulusBending BeamsIn the MomentWhat’s it take to bend it?Energy in the bent beamCalculating beam deflectionTallying the forces/momentsA Simpler ExampleWhat’s the deflection?Calculating the curveBending Curve, IllustratedEnd-loaded cantilever beamSimply-supported beam under own weightSimply-supported beam with centered weightS-flex beamCantilevered beam formulaeSimply Supported beam formulaeLessons to be learnedGetting a feel for the I-thingyMoments LaterAnd more momentsThe final momentLessons on momentsBeyond ElasticityBreaking StuffNotes on Yield StressShear StressPractical applications of stress/strainApplications, continuedFlexure DesignFlexure Design, cont.Notes on Bent Member Flexure DesignKinematic DesignBasic PrinciplesDiamond Pin IdeaKinematic SummaryReferences and AssignmentMaterialsMaterialsPropertiesPropertiesMechanicsMechanicsWinter 2012UCSD: Physics 121; 20122Why we need to know about materialsWhy we need to know about materials•Stuff is made of stuffStuff is made of stuff–what should your part be made of?–what does it have to do?–how thick should you make it•The properties we usually care about are:The properties we usually care about are:–stiffness–electrical conductivity–thermal conductivity–heat capacity–coefficient of thermal expansion–density–hardness, damage potential–machine-ability–surface condition–suitability for coating, plating, etc.Winter 2012UCSD: Physics 121; 20123Electrical ResistivityElectrical Resistivity•Expressed as Expressed as  in in ·m·m–resistance = ·L/A •where L is length and A is area–conductivity is 1/Material (10-6 ·m)commentsSilver 0.0147 $$Gold 0.0219 $$$$Copper 0.0382 cheapest good conductorAluminum 0.047Stainless Steel 0.06–0.12Winter 2012UCSD: Physics 121; 20124Thermal ConductivityThermal Conductivity•Expressed as Expressed as  in W m in W m-1-1 K K-1-1–power transmitted = ·A·T/t, •where A is area, t is thickness, and T is the temperature across the materialMaterial (W m-1 K-1)commentsSilver 422 room T metals feel coldCopper 391 great for pulling away heatGold 295Aluminum 205Stainless Steel 10–25 why cookware uses S.S.Glass, Concrete,Wood 0.5–3 buildingsMany Plastics ~0.4 room T plastics feel warmG-10 fiberglass 0.29 strongest insulator choiceStagnant Air 0.024 but usually moving…Styrofoam 0.01–0.03 can be better than air!Winter 2012UCSD: Physics 121; 20125Specific Heat (heat capacity)Specific Heat (heat capacity)•Expressed as cExpressed as cpp in J kg in J kg-1-1 K K-1-1–energy stored = cp·m·T•where m is mass and T is the temperature changeMaterial cp (J kg-1 K-1) commentswater 4184 powerhouse heat capacitoralcohol (and most liquids) 2500wood, air, aluminum, plastic 1000 most things!brass, copper, steel 400platinum 130Winter 2012UCSD: Physics 121; 20126Coefficient of Thermal ExpansionCoefficient of Thermal Expansion•Expressed as Expressed as  = = LL//LL per degree K per degree K–length contraction =  ·T·L,•where T is the temperature change, and L is length of materialMaterial (10-6 K-1)commentsMost Plastics ~100Aluminum 24Copper 20Steel 15G-10 Fiberglass 9Wood 5Normal Glass 3–5Invar (Nickel/Iron alloy) 1.5 best structural choiceFused Silica Glass 0.6Winter 2012UCSD: Physics 121; 20127DensityDensity•Expressed as Expressed as  = = mm//VV in kg·m in kg·m-3-3Material (kg m-3)commentsPlatinum 21452Gold 19320 tell this to Indiana JonesLead 11349Copper, Brass, Steels 7500–9200Aluminum Alloys 2700–2900Glass 2600 glass and aluminum v. similarG-10 Fiberglass 1800Water 1000Air at STP 1.3Winter 2012UCSD: Physics 121; 20128Stress and StrainStress and Strain•Everything is a spring!Everything is a spring!–nothing is infinitely rigid•You know Hooke’s Law:You know Hooke’s Law:F = k·L–where k is the spring constant (N/m), L is length change–for a given material, k should be proportional to A/L–say k = E·A/L, where E is some elastic constant of the material•Now divide by cross-sectional areaNow divide by cross-sectional areaF/A =  = k·L/A = E·  = E· = E·–where  is L/L: the fractional change in length•This is the stress-strain law for materialsThis is the stress-strain law for materials is the stress, and has units of pressure is the strain, and is unitlessWinter 2012UCSD: Physics 121; 20129Stress and Strain, IllustratedStress and Strain, Illustrated•A bar of material, with a force A bar of material, with a force FF applied, will change its size by:applied, will change its size by:L/L =  = /E = F/AE•Strain is a very useful number, being Strain is a very useful number, being dimensionlessdimensionless•Example: Standing on an aluminum Example: Standing on an aluminum rod:rod:–E = 70109 N·m2 (Pa)–say area is 1 cm2 = 0.0001 m2–say length is 1 m–weight is 700 N = 7106 N/m2 = 104  L = 100 m–compression is width of human hair FFALL = F/A = L/L = E·Winter 2012UCSD: Physics 121; 201210Elastic ModulusElastic Modulus•Basically like a spring constantBasically like a spring constant–for a hunk of material, k = E(A/L), but E is the only part of this that is intrinsic to the material: the rest is geometry•Units are N/mUnits are N/m22, or a pressure (Pascals), or a pressure (Pascals)MaterialMaterialE (GPa)E (GPa)Tungsten 350Steel 190–210Brass, Bronze, Copper 100–120Aluminum 70Glass 50–80G-10 fiberglass 16Wood 6–15most plastics 2–3Winter 2012UCSD: Physics 121; 201211Bending BeamsBending Beams•A bent beam has a stretched outer surface, a compressed inner A bent beam has a stretched outer surface, a compressed inner surface, and a neutral surface somewhere betweensurface, and a neutral surface somewhere between•If the neutral length is If the neutral length is LL, and neutral radius is , and neutral radius is RR, then the strain , then the strain at some distance, at some distance, yy, from the neutral surface is (, from the neutral surface is (R + yR + y)/)/R R  1 1 = y/R–because arclength for same  is proportional to radius–note L = R•So stress at So stress at yy is is  = =