Aircraft Structures for Engineering Students 7th Edition T. H. G Megson | Solutions Manual

Aircraft Structures for Engineering Students Seventh Edition Solutions Manual Solutions to Chapter 1 Problems S.1.1 The principal stresses are given directly by Eqs (1.11) and (1.12) in which σx¼80 N/mm2, σy¼0 (orAircraft Structures for Engineering Students Seventh Edition Solutions Manual Solutions to Chapter 1 Problems S.1.1 The principal stresses are given directly by Eqs (1.11) and (1.12) in which σx¼80 N/mm2, σy¼0 (or vice versa), and τxy¼45 N/mm2. Thus, from Eq. (1.11), σI ¼ 80 2 + 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p802 + 4452 i.e., σI ¼ 100:2 N=mm2 From Eq. (1.12), σII ¼ 80 2  1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p802 + 4452 i.e., σII ¼ 20:2 N=mm2 The directions of the principal stresses are defined by the angle θ in Fig. 1.8(b) in which θ is given by Eq. (1.10). Hence, tan2θ ¼ 245 800 ¼ 1:125 which gives θ ¼ 24°110 and θ ¼ 114°110 It is clear from the derivation of Eqs (1.11) and (1.12) that the first value of θ corresponds