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# Biomechanics I Kaap426 Exam 2 Material KAAP426

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This 33 page Study Guide was uploaded by Kgayton@udel.edu Notetaker on Wednesday September 16, 2015. The Study Guide belongs to KAAP426 at University of Delaware taught by Dr. Royer in Spring 2015. Since its upload, it has received 82 views. For similar materials see Biomechanics I in Physical Education at University of Delaware.

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Date Created: 09/16/15

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9Q boNu 0me quotxg ona e 5 e e 5 h 7 7 7 iwi M RAN LL quot 1quot wmw 4WD QM Yaw DAR 80m 2 RN 5amp1 NCM 2quot FM 11333 L U 193i 29 7 r r 7 F A f LEM til QOQN 18m 3 FHUSCK KAAP 426 Biomechanics Problem Set 2 Completing this problem set is voluntary however you are encouraged to work through the problems in preparation for the next exam Solutions will be provided in class For each problem consider what information is given what the problem is asking for then determine what equationss will get you there Be careful to keep your units consistent and don t forget to attach the correct units to your answer 1 A compressive force of 6000N is applied to a bone that has an outside radius of 26 cm and a hollow inside radius of 22 cm A Calculate the compressive stress of this bone answer 995 NcmZ or 9950000 Nm2 or Pa or 995MPa B What is the maximum force this bone can withstand in compression before failing if the maximum compressive stress of cortical bone is 200 MPa Be careful with your units answer 120570 N 2 Now a bending moment of 200 Nm is applied to the same bone outside radius 26 cm inside radius 22 cm A Calculate the maximum bending stress of this bone answer 2974 Ncmz or 29740000 Nrn2 or Pa or 297 MPa B Calculate the bending stress at the internal edge of the bone material answer 2516 Ncmz or 25160000 Nm2 or Pa or 251 MPa 3 A bending moment of 250 Nm is applied to a solid bone with a radius of 19 cm Calculate the bending stress that occurs 12 cm from the neutral axis answer 2932 Ncmz or 29320000 Nm2 or Pa or 293 MPa 4 A bending moment of 180 Nm applied to a hollow bone outside radius 27 cm inside radius 20 cm results in a maximum bending stress of approximately 167 x 106 Nmzz A Calculate the radius of a solid bone necessary to withstand this maximum bending stress answer 00239 m or 239 cm B How much larger is the area of the solid bone you found in 4A compared to the solid ring area of the hollow bone expressed as a percentage increase relative to the hollow bone Write one thoughtful sentence about the result answer 73 larger increase larger smaller smaller times 100 Bone Structure Cortical bone low porosity 530 of bone volume is occupied by nonmineralized tissue Cancellous or trabecular bone high N porosity 30 90 of bone volume is occupied by non mineralized tissue Stress and strain Stress load or force per unit area Computationally equivalent to pressure a sigma F once a 2 2 f A area Units Nm 2 or Pascal Strain normalized deformation that occurs at a point in a structure in response to an externally appHedload a epsilon g Ag i change in length E original i Z en gth 0 Units or unitless bone Defermation Mechanical properties of bone Hypothetical load defOrmation curve A begin test no load yet so no deformation B 2 yield point deformation is permanent past yield C Ultimate failure test ends A to B Elastic region B to C Plastic region Load Deformation Strain example Normal or linear strain change in length as a or proportion of original length eg a bone tissue sample with an original length of 10 cm is elongated to 107 cm before fracture The ultimate strain is 7 Bone Fracture Cortical bone Can withstand greater stress than cancellous but Fracture at 2 strain Cancelious bone Fracture at 75 strain Both types of bone are anisotropic Mechanical properties change when loaded in different directions Anisotropic behavior Stress 0 Strain a Example Toothpick 1 Loading modes 1 Q Tension Unloaded Compression Torsion f f Shear f Bending Loading modes Cortical bone Bones are strongest under compressive loads and weakest undersheanngloads Compare cortical vs cancellous bone under compression and tension Stress MP3 250 l 200 150 100 j 50 l Compression Tension D Shear D Cancellous Mode Cool design features of bone Why are bones shaped the way they are flared out at the ends and tapered in the middle 7 39 g gt l A a r 39 it 5 a WP i hi i 1 l A f 4 quota39 7s 1quot b l Why are bones hollow 39 39 10 Influence of bone size and shape For tension and compression the load to failure is proportional to the crosssectional area Femur High forces and large Xsectional area Ff0r O Radius Low forces and small Xsectiona1 area A area 11 0111222 cm U Solid area of a ring or circle cylinder A 72rour side Firaside A 7r3cm2 2cm2 71395c mz157cm2 ring A W2 7r cmgt21157cm2 Circle 12 Influence of bone size and shape For bending loads the area moment of inertia is most important a Length is also a factor Area moment of inertia takes into account crosssectional area distribution of material about a neutral axis these two figures have the same solid cross sectional area but different area moment of inertia 13 Area Moment of Inertia cylinder Resistance to bending Describes the region of the bone regardless of where you are calculating stress 14 Area Moment of Inertia rectangl w 3 I 2 P22 12 h2in 8i neutral axis L b8 in a b2 In 3 3 x 18X2 Eil 531714 1 2X8 3 19241quot 2 12 12 12 12 example floorjoists 15 times Stronger 15 Back to tubular material For a given bending moment Mr M applied to a structure the 0 T stress depends on both the as increases 6 T applied moment and on the distance away r from the neutral axis as increases 0 T as increases 6 L compression tension e w I neutral aXls tension l l 16 Influence of bone size and shape Hollow 656W out in I r4 r4 I3cm4 26m4 I 7 Jill1mx 100Ncm3cm O 0 7 7 4 1 I 510m Solid 7 4 7r 4 256m47r 4 121 1216 56m 1 4 1196cm nax 100Ncmxgcm i 114N 0 039 4 i 0 2 I 196cm cm A given moment I OONcm produces less bending stress in the hollow bone vs soiid bone with the same bone material area 5101714 17 Fracture Healing After fracture and during the healing process a cuff of callus forms around the site This serves the following purposes Increases cross sectional area Increases area and polar moments of inertia The general result is an increase in strength and stiffness of an otherwise weak spot on bone 39 Once healing is complete the cuff is resorbed 19 Influence of muscle activity on stress distribution in bone Unleaded Fixed and subject to 3pt bending 20 Influence of muscle activity on stress distribution in bone Fixed and subject to Fixed and subject to 3 pt bending 3 pt bending with muscle Therefore muscle serves to protect bone from fracture muscles add compressive force reduces bone tension Femoral Neck Example weight of weight of upper body upperbody 3 gluteus med ius no musculature reduced teon 22 Repetitive loading and fatigue Bone tissue fatigue is affected by magnitude of load number of applied loads rate of loading Typically sustained during continuous strenuous exercise when muscles are fatigued why Load Repetition 23 Bone remodeling Wolff s Law 1892 one adapts to the loads that are placed uponit Architecture Mineral content Material properties Major factors affecting bone remodeling Activity Disease Age 24 Bone Hypertrophy Examples Child born with one tibia Tennis player baseball pitcher arm Olympic athletes weight lifters vs swimmers Short folks vertically chalenged who want to become taller Magnitude of loading rather than frequency of loading is related to bone mass 25 Bone Atrophy Reduced loads on the body bedridden patients sedentary senior citizens astronauts 39 How can we add gravity in space spinning space station centrifuge treadmill running with bungee cords 26 Bone remodeling siliir l if quot quot 49quot H g iw lhgl 1 UV Inhi ip hd L1 fpifi li a l ig quotnil r 7 a g L w tan 11 J I quot 1 27 Young vs old Ultimate stress was Young similar between young and oid c Uitimate strain for oider bone was half as large as younger bone Greater brittleness Reduction in energy f f Strain storage capacity Stress Normal vs immobilized Kazarian amp Von Gier ke 1969 Rhesus monkeys immobilized in fullbody casts for 60 days Similar strains at failure Ultimate stress and energy storage was 3gtlt higher in normals Stiffness also higher in normals Load Normal Immobilized Deformation 29

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