1) human long bones are exposed to complex loading states during nomal activities. analyzing the stresses and stra ins with in bone tiss ue often requires computational mode ls or experiments; however a first-order beam analysis of the combined loading state may often be appropriate to obtain estimates of stresses in the m id-d ia physis. cons id er the following example and carefully list all the neces sary assumptions. one of the assum ptions needs to be that the bone behaves as an isotropic material. under a state of loading approximating that in a moderate knee bend, the femur is exposed to loads at the distal end due to contact with the tibia and patella. for the purposes of this analysis we will neglect all direct muscle forces, but include the contribution of muscle activity through the magnitudes of the contact forces considered. we are interested in calculating the stresses at 4 points on the outer surface of the bo ne, a distance 8 away from the distal end. suppose we have done our static ana lysis and obtain ed resultant tibio-femoral joint contact forces of 3 times body weight and patellar contact forces of 2 times body we ig ht. however, because of the alignment of the lower limb during loading, the tibio-fem oral load is split into two different contact points of unequal magnitude. assume that the medial contact force is 2bw and the lateral contact force is 1bw. the cross-se ctio nal dimensions of the femur at the point of interest may be approximated as a circular cross-section, with outer diameter 1.5" and inner diameter 0.75". assume that the patella force pushes at an angle of 45 with respect to the long axis of the bone (towards the posterior direction). the two tibio-femoral joint contact forces act through the midpoint of the medial and lateral condy les -each 0.75" away from the midd le of the femur shaft consider the medial force to be 2 tim es body weight and the lateral force to be 1 times body weight. each may be considered to act along the axis of the tibia shaft, with a knee flexion angle of 30° from full extension. assume body weight is 150 lbs. sketch the bone clearly from multiple angles, to be sure you understand this loading condition. ideally, represent the bone in 3d (x-y-z coordinate system). make the x axis along the medial-lateral direction , the y axis along the inferior-superior direction (along the long axis of the bone), and the z axis along the anterior- posterior direction. to perform the beam analysis, you may consider the proximal end of the femur essentially fixed in space. you may need to consid er torsion al, bending, axial and shear loads in this example. sum these combined effects in an appropriate manner. list all variables carefully and any estimated dimensions you might need. calculate the state of stresses on the anterior, posterior, medial and lateral outer surfaces of the mid-diaphysis, first with respect to axis oriented along the long axis of the bone, then calculate the magnitude and direction of principal stresses and maximum shear stresses. comment on the result and compare the calculated stresses with the known strength of cortical bone.