Question

3. (20 pts) For stresses a= 10 kpsi, az = -15 kpsi, txy 5 kpsi, Cw. (3.1) (14 pts) Calculate all principal normal and shear stresses G1, 02, 03, Ti2, T2s, T1s (3.2) (6 pts) Draw a complete 3D Mohr's circle diagram and label points ot, 02, 03, T1/2, T23, T1s an below with all dimensions in inches. The beam + the ton

Answer 1

stresses 6x6 = 10 kpsi by=iskosi exey - skepsi to calculate principal normal tan 20p= 2zry- and sheal shesses 6,2 = 'farby & J ( Exty) , zay - tog 20s= woman os: op 1450 6 = 11 sata kpsi 62 = 0 63 = -16 kpsi op 1009 deg Zmax= 13.5 Hlaupi Zg = 8 oss = ssog - Zz = 5.5 QS2 = -34./ * Daire

Characteristic polynomial equation 03-A02+Bo-C=0 Polynomial coefficient (A) =0x+Oy+Oz =0'1+0'2+03 Polynomial coefficient (B) =0x0y+ Oy0z+OxOz-(Txy)2-(tyz)2-(tx2)2 =0'10'2+0 20'3+0'10'3 Polynomial coefficient (C) = OxOy Oz+2Tyytyzxz-Ox(Tyz)2-Oy (Txz)2-Oz (Txy)2 =0'10'20'3 Principal stress-1 (01) max(o 1,02,03) Principal stress-2 (02) A-01-02 Principal stress-3 (03) min(oʻ1,0'2.0'3) Max shear stress - 1 (Tmax1) (02-03)/2 Max shear stress -2 (Tmax2) (01-03)/2

MOHR'S CIRCLE FOR 3D STRESS [MPa] RESULTS Principal Stresses (-16, 0) (0,0) 11, 0) Maximum Shear Stresses (-8,8) -2.5, 13.5) 5.5,5.5) www.amesweb.info