a) Determine the buckling critical load for a 2.5 meter column which is fixed at both ends if E=15GPa. The diameter of the column cross section is 300mm. b) Calculate the principal strains, given that the state of plane strain for an element is: x=25micronsy=100micronsxy=45microns c) Briefly outline how materials fail due to fatigue. Support your answer using a typical S-N graph. d) The steel plate shown in Figure Q1(d) has a 40mm crack which is normal to the direction of the load of 90kN. Material tests indicate that its Mode 1 critical stress intensity factor is 25MPa.m. The thickness of the plate is 15mm. Determine if the plate will experience unstable crack propagation. Polar moment of inertia of shaft: Solid: J=2c4 Hollow: J=2(c04ci4) Solid shaft second moment of inertia: I=64d4 Shaft shear stress: max=JTcor=JT Shaft angle of twist: =JGTL Transformation of plane stress: x=2x+y+2xycos2+xysin2y=2x+y2xycos2xysin2xy=2xysin2+xycos2 Principal Stresses: 1,2=2x+y[2xy]2+xy2 Principal Plane: tan2p=xy2xy Page 7 of 9 Principal Strains: 1,2=2x+y(2xy)2+(2xy)2 Plane of principal strain: tan2p=xyxy Deformation due to axial loading : =AEPL Eulers Formula for critical load: Pcr=Le22EI Eulers Formula for critical stress: cr=(Le/r)22E Cylindrical Pressure Vessels: hoop=tprlong=2tpr Power to torque relationship: P=2fT Keyways: LS=SytDW4TNfsLB=KSycDH4TNfS Critical length of edge crack: a=1(SyKlc)2 Gear power and loads: Wt=dn60(10)3H Page 8 of 9 Stress concentration factor charts