Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driveris 10 inches, find the center distance between cylinders. A. 15 in B. 10 in C. 25 in. D. 20 in. Please solve the Problem elaborately. Your solution will be use as reference for my studies. Thank you so much your work will be appreciated much! Machine Elements1. Cylinders Rolling in opposite direction:A. Tangential speed V = Va =n D. N == D, N:D. N. = D. NaB. Relation of diameter and speedSpeed of DriverSpeed of the DrivenC. Speed Ratio=D. Center Distance- R, + R, D, + D222. Cylinders Rolling in the same directionA. Tangential speed VVn D, N = D, N,B. Relation of diameter and speed D: N = D, NaSpeed of DriverSpeed of the Driven.C. Speed Ratio =D. Center Distance = R, -R,- D-D,2Stresses1. Stress (S) = a total resistance that a material offers to an applied load, Ibin, kg/cm, KN/m?2. Ultimate stress (S.) - is the stress that would cause failure3. Yield stress(S,) - maximum stress without causing deformation4. Allowable stress(Sa) = Ultimate stress/Factor of Safety5. Design stress(S.) - stress used in determining the size of a member. S= or S=where: FS factor of safety1. Tensile Stress (S)S = 4For solid circular cross-section: A = DFor hollow circular cross-section: A = (D, -D)For rectangular cross-section: A = base x height = b xh2. Compressive Stress(S.)S.3. Shearing Stress(S.)A. For single bolt of rivet needed to join to plates together. S, =For single rivet: A= z4 DFor double riveted joint: A= 2(m/4 D)where:B. Shearing due to punching of hole.S= where A DI (for punching a hole) A4S1 (for square hole)Where: S= length of side oft= plate thicknessWhere: d= hole diameter, in4. Bearing Stress(S) S, F IAC. Pressure needed to punch a hole, F: Fdxtx 80, tonst= thickness, inwhere: A= DLShea aa5. Factor of safety(FS) a. Based on yield strength FS = S, /Sb. Based on ultimate strength FS = s./ S6. Torsional Shear Stress(S.)Projected Areawhere: J = polar moment of inertia = T D' /32 (for solid shaft)T= torque c - distance from neutral axis to the farthest fiberC-r (for circular cross section)d- diameter6 M7. Bending Stress(S)S- For rectangular beam Sbhwhere: M = momentC= distance of farthest fiber from neutral axis|- moment of inertia about the neutral axis= bh/12 (for rectangular cross section)Z = section modulus =c S8. Strain and Elongation Strain = !E. Stress . FLStrainY= FLAEStress a F- AVL- original lengthS stresswhere: y- elongation due to applied loadF force A area9. Thermal Elongation; Stressesy = kL (t - t:) s = EL = kE (t - t)where: k = coefficient of thermal expansion, m/m-CFor steel k- 6.5 x 104 inin-F- 11.7 x 104 m/m-CE = 30 x 10 psiRelation betwoen shearing and tensile stress based on theory of failure:Suna- Sy 12Swa- S10. Variable Stress1. S.FS S, S.S, - yield pointS = mean stresswhere: FS = factor of safetyS. endurance limitSmax + SnS. = variable component stressS.. maximum stressSen minimum stress11. Poisson's Ratio(u) = is the ratio of lateral unit deformation to axial unit deformation.FE- strain=AEwhere: G = shear modulus of elasticity2GLateral StrainWa-WLongitudin al StrainE, -LE, Ex

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