东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A18 Combined Loading

DE:Resolvethe couple vector into components andcalculate the corresponding maximum stresses.1600lb.in.M,=(16001b·in)cos30=13861b·inM,=-(16001b·in)sin30=-800lb·inZCN1, =(1.5 in)(3.5in) = 5.359in46=30°1.75 in.I, =(3.5in)(1.5in) =0.9844in4The largest tensile stress due to M, occurs along ABBAM.y_ (13861b·in)(1.75in)=452.6psir1.5.359in40.75 inThe largest tensile stress due to M, occurs along ADM.z(-8001b·in)(-0.75in)= 609.5psi0210.9844in4.Thelargesttensilestressduetothecombinedloading occurs at A.Omax =O, +, = 452.6+609.5=1062psi11

• Resolve the couple vector into components and calculate the corresponding maximum stresses.              3 1 4 12 3 1 4 12 1 4 1600lb in cos30 1386lb in 1600lb in sin 30 800lb in 1.5in 3.5in 5.359in 3.5in 1.5in 0.9844in The largest tensile stress due to occurs along 1386lb in 1.75in 452.6ps 5.359in z y z y z z z M M I I M AB M y I                       2 4 i The largest tensile stress due to occurs along 800lb in 0.75in 609.5psi 0.9844in z y y M AD M z I        • The largest tensile stress due to the combined loading occurs at A. max 1 2         452.6 609.5 1062psi z y 11

DeterminetheangleoftheneutralaxisM,2oM.yo(13861bin)+(800b-in)=258.63y812.680=0x145.359in40.9844812.68yo=3.142tand=258.63ZoΦ=72.4°E1062psiDDEZXISYo,=o)BA2B1062psi12

• Determine the angle of the neutral axis. 0   0 0   0 4 0 0 0 0 1386lb in 800lb in 0 258.63 812.68 5.359in 0.9844 812.68 tan 3.142 258.63 72.4 z y x z y o M y M z y z y z I I y z                  12 z y   y z 0 0 , 