L02 - Load and stress analysis 302315 L02 - Load and stress analysis

Identify critical cross sections Principle stress determination Load analysis Assume materials to be homogeneous and isotropic Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD Load termination Based on the load distribution, determine what cross sections of the part are most heavily loaded. Identify critical cross sections (SFD, BMD) Determine the stress distribution over the cross section of interest. Locate the highest of applied and combine stresses Stress determination identify state of stress at a points of interest Stress element Calculate the principal stresses and maximum shear stress Principle stress determination Calculate the critical deflection of the part Critical Deflection Failure criteria

Crimping tool-static loading

FBD Link3 Link4 Link2

15 varibles; 13 equations 1) F12x + F32x = 0 2) Fh + F12y + F32y = 0 3) RhFh + (R12xF12y - R12yF12x) + (R32xF32y – R32yF32x) = 0 4) F23x + F43x = 0 5) F23y + F43y = 0 6) (R23xF23y – R23yF23x) + (R43xF43y – R43yF43x) = 0 7) Fc4x + F34x + F14x = 0 8) Fc4y + F34y + F14y = 0 9) (Rc4xFc4y – Rc4yFc4x) + (R34xF34y – R34yF34x) + (R14xF14y – R14yF14x) = 0 Link2 Link3 Link4 10) F32x - F23x = 0 Given 11) F32y - F23y = 0 12) F43x - F34x = 0 13 varibles; 13 equations 13) F43y - F34y = 0

Cross product Mz= (RxFy-RyFx) Moment = R x F (+) i (-) j (+) k Rx Ry Rz Fx Fy Fz M = Mxi + Myj + Mzk i j k Rx Ry Rz Fx Fy Fz i j k Rx Ry Rz Fx Fy Fz i j k Rx Ry Rz Fx Fy Fz Mxi = (RyFz-RzFy)i Myj = - (RxFz-RzFx)j Mzk = (RxFy-RyFx) k In 2 - D (+) i (-) j (+) k Rx Ry Fx Fy Mx= 0 Mz= (RxFy-RyFx) My = 0

Assignment AS01

Solving system of linear equations Inverse matrix Cramer’s rule Gaussian elimination

solution Force geometric data 1 Fh 0.236 kN Rh -111.76 mm 2 F12x 6.732 R12x 35.56 3 F12y -1.695 R12y 1.27 4 F32x -6.732 R32x 55.88 5 F32y 1.459 R32y 2.032 6 F23x R23x -15.24 7 F23y -1.459 R23y 3.302 8 F43x R43x 15.24 9 F43y R43y -3.302 10 F34x R34x 4.064 11 F34y R34y 19.304 12 F14x 1.969 R14x -4.064 13 F14y -0.390 R14y -19.304 14 Fc4x -8.701 Rc4x 11.43 15 Fc4y 1.849 Rc4y 8.636 16 Fc1x 8.701 Rc1x   17 Fc1y -1.849 Rc1y 18 F21x R21x 19 F21y 1.695 R21y 20 F41x -1.969 R41x 21 F41y 0.390 R41y solution

matrix

Link 3 – compression load

Link 4 – bending load

Combine load

Load Static load dynamic load Impact load Vibration Beam load Type Load termination Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD dynamic load Impact load Vibration Beam load Type location direction Time-variation Magnitude concentrate force duration distribute continuation torque uniform moment non-uniform

Stress analysis Column and Beam

Identify critical cross sections Principle stress determination Stress analysis Assume materials to be homogeneous and isotropic Determine all applied loads (forces, moments, torques) and present where those appear on the part’s geometry using FBD Load termination Based on the load distribution, determine what cross sections of the part are most heavily loaded. Identify critical cross sections (SFD, BMD) Determine the stress distribution over the cross section of interest. Locate the highest of applied and combine stresses Stress determination identify state of stress at a points of interest Stress element Calculate the principal stresses and maximum shear stress Principle stress determination Calculate the critical deflection of the part Critical Deflection Failure criteria Calculate Von Mises effective stress at each selected point based on the principal stresses Trial on a material Compute safety factor based on tensile yield strength of that material DUCTILE MATERIALS Calculate Coulomb-Mohr effective stress at each selected stress element based on its principal stresses Compute safety factor based on ultimate tensile strength of that material BRITTLE MATERIALS

Stress component sxx txy txz tyx syy tyz tzx tzy szz sxx txy tyx syy

transformation stress

Normal stress The plane at which zigma is max, shear stress is zero

SHEER STRESS The plane at which shear stress is max,

Principal stress https://youtu.be/6mWlkqfAjz8?list=PLLbvVfERDon3oDfCYxkwRct1Q6YeOzi9g

Mohr’s circle 2-D https://youtu.be/WOCFY4gnTyk https://youtu.be/8NczBbo8_04 3-D https://youtu.be/9x6lpkap9qs

Assignment Dynamic load Stress in Beam

Dynamic loading Fx = max Fy = may Mz = Izz dynamic analysis Fz = maz Mx = Ixx – (Iy-Iz)yz My = Iyy – (Iz-Ix)zx Mz = Izz – (Ix-Iy)xy 2-D in x-y plane Fx = max Fy = may Mz = Izz

caSE : Link 4 STRESS IN BEAM

Shear stress SFD – Sheer force diagramj

Stress due to bending BMD – Bending moment diagramj