Calculate the strain and change of length of the femur during a single step while running. (Use t described in the discussion near equation 4.21) Energy Storage in Tendons and Long Bones Let us return to the example of running in Fig. 3.34 [2]. The force on the Achilles tendon is 4,700N. With a cross-sectional area of 89 mm², we see that 4,500 N/89 mm² = 53 N/mm² = 53 MPa. Given the maximum stress for tendons, the UTS, is ~100 N/mm² = 100MPa, during running the stress in these tendons is not far from the damage threshold. It is not surprising that the Achilles tendons of athletes occasionally snap, either partially or totally. Using the stress-strain relation shown in Fig.4.14, this stress leads to a strain of 0.06 6%. The length of the Achilles tendon is Lo= 250mm, so this strain corresponds to the tendon lengthening by 15 mm and -TJE Va+AL=(53 N/mm = 35,000 N-mm = 35 N-m = 35 J. PE= Clamp This is exactly the amount of energy we stated was being stored in the Achilles tendon during every step of a run. How much energy is stored in the bones during this step? Let us examine the largest bone, the femur. We will use Lo 0.5 m and so V 165,000 mm³. Also Y = 500 mm and A = 330 mm². - 17, 900 MPa = 17,900 N/mm². The upward Tendon Load cell to -Extensometer Tit (53 -Actuator N/mm²)(0.06) (89 mm²) (250 mm) (4.18) (4.19) Stress (newtons per square millimetre) 60- 40- 0 = Strain (%) Fig. 4.14 Stress-strain (or force-length) for a human big toe flexor tendon, using the instrument on the left, with a 2-s-long stretch and recoil cycle. (From [2]. Copyright 1992 Columbia University Press. Reprinted with the permission of the Press)