#1. A hollow circular shaft with an outer diameter of 80 mm and an inner diameter of 50 mm is subjected to a combined bending moment of 4.5 kN·m and a torque of 3.2 kN·m. Using the von Mises criterion, determine the equivalent stress at the outer surface.
#2. A thick-walled cylinder with inner radius 60 mm and outer radius 100 mm is subjected to both internal pressure of 80 MPa and external pressure of 20 MPa. Determine the maximum tangential stress in the cylinder wall.
#3. A stepped shaft has diameters of 50 mm and 40 mm with a fillet radius of 4 mm. The shaft transmits a torque of 600 N·m. If the theoretical stress concentration factor Kt = 1.45 and the notch sensitivity q = 0.85, determine the maximum shear stress at the fillet.
#4. A bolted joint with four M12 bolts (At = 84.3 mm² each) connects two flanges. The joint stiffness ratio C = 0.28. If the external load varies from 10 kN to 40 kN, and the initial preload per bolt is 20 kN, determine the maximum stress in each bolt.
#5. A compound cylinder is formed by shrink-fitting a steel outer cylinder (ri = 75 mm, ro = 100 mm) onto a steel inner cylinder (ri = 50 mm, ro = 75 mm). The interface pressure after assembly is 40 MPa. Determine the hoop stress at the inner surface of the inner cylinder when an internal pressure of 60 MPa is applied.
#6. A helical compression spring operates between a minimum force of 200 N and maximum force of 500 N. The wire diameter is 6 mm, mean coil diameter is 42 mm, and G = 79.3 GPa. If the spring has 12 active coils, determine the endurance stress amplitude using the Zimmerli approach with a fatigue factor of 0.5.
#7. A rotating shaft is supported by two identical ball bearings spaced 400 mm apart. A gear mounted 100 mm from the left bearing exerts a radial force of 8 kN and an axial thrust of 3 kN on the shaft. Using X = 0.56 and Y = 1.4 for both bearings, determine the equivalent dynamic load on the more heavily loaded bearing.
#8. A power screw with a mean diameter of 44 mm and a double-start thread (lead = 12 mm) raises a load of 50 kN. The thread friction coefficient is 0.14 and the collar friction coefficient is 0.08 with a collar mean diameter of 70 mm. Determine the total torque required to raise the load.
#9. A cantilever beam of length 800 mm has a T-section with the following dimensions: flange width 80 mm, flange thickness 12 mm, web height 60 mm, web thickness 10 mm. A load of 5 kN is applied at the free end. Determine the maximum tensile bending stress in the beam.
#10. A component is subjected to variable amplitude loading described by rainflow counting: 2000 cycles at Sa = 200 MPa (Nf = 10⁴), 5000 cycles at Sa = 150 MPa (Nf = 5×10⁴), and 50000 cycles at Sa = 80 MPa (Nf = 10⁶). Determine the remaining life fraction according to Miner’s rule.
#11. A circular fillet weld pattern with a mean radius of 60 mm and leg size of 8 mm is subjected to both a vertical shear force of 25 kN and a torque of 3000 N·m about its centroid. Determine the maximum resultant shear stress in the weld.
#12. A shaft-hub press fit must withstand a torque of 1200 N·m and an axial force of 20 kN simultaneously. The shaft diameter is 70 mm, fit length is 60 mm, and friction coefficient is 0.15. Determine the minimum required interface pressure.
#13. A simply supported beam with a rectangular cross-section (b = 60 mm, h = 100 mm) and span of 2 m carries a uniformly distributed load w and a concentrated load P = 2w·L at mid-span. If the maximum allowable bending stress is 150 MPa, determine the maximum allowable value of w.
#14. A planetary gear train has a sun gear with 30 teeth, three planet gears with 20 teeth each, and a ring gear. The planet carrier is the input rotating at 1000 rpm, and the ring gear is fixed. Determine the output speed of the sun gear.
#15. An ACME threaded power screw (included angle 29°) has a pitch diameter of 38 mm and a pitch of 8 mm. The coefficient of friction is 0.13. Determine the efficiency when raising a load, accounting for the thread angle effect.
#16. A machine component is subjected to completely reversed bending stress. The component has Sut = 700 MPa, a machined surface (ka = 0.78), size factor kb = 0.82, reliability factor kc = 0.897 (99% reliability), and operates at an elevated temperature (kd = 0.87). A stress concentration exists with Kt = 2.1 and q = 0.75. Determine the corrected endurance limit.
#17. A curved beam with a rectangular cross-section (width 40 mm, depth 60 mm) has an inner radius of 100 mm. A bending moment of 4 kN·m is applied tending to increase the curvature. Determine the maximum bending stress at the inner fiber.
#18. A bolted pressure vessel flange uses 16 M20 bolts (At = 245 mm² each) equally spaced on a 400 mm bolt circle. The vessel internal diameter is 300 mm, operating pressure is 6 MPa, and gasket factor m = 2.5. Determine the required bolt preload per bolt for proper sealing.
#19. A welded bracket consists of two horizontal fillet welds (150 mm each) and two vertical fillet welds (100 mm each) forming a rectangular pattern. A horizontal force of 60 kN is applied at a distance of 200 mm from the weld group centroid. Determine the leg size required if the allowable shear stress is 110 MPa.
#20. A multi-disc clutch has 4 friction discs (8 friction surfaces) with outer radius 120 mm and inner radius 80 mm. The coefficient of friction is 0.32 and the axial clamping force is 5 kN. Using uniform pressure theory, determine the torque capacity.
#21. A thin-walled pressure vessel with hemispherical ends has a cylindrical section diameter of 1.2 m and wall thickness of 18 mm. The vessel is made of steel (E = 200 GPa, ν = 0.3) and subjected to internal pressure of 5 MPa. Determine the maximum principal strain in the cylindrical section.
#22. A splined shaft has 8 rectangular splines with major diameter 56 mm and minor diameter 46 mm. The engagement length is 80 mm and the allowable bearing pressure is 15 MPa. If only 75% of the spline length is effective due to misalignment, determine the torque capacity.
#23. A toggle mechanism uses a pin of 18 mm diameter passing through a clevis with two arms of 15 mm thickness each. The maximum load during toggle action reaches 35 kN. Determine the factor of safety against shear failure if the pin material has an ultimate shear strength of 320 MPa.
#24. A shaft transmits 50 kW at 600 rpm. The shaft material has an ultimate tensile strength of 600 MPa and a yield strength of 400 MPa. Using the ASME code with Cm = 1.5 (shock and fatigue for bending) and Ct = 1.0, determine the minimum shaft diameter.
#25. Two helical compression springs are nested concentrically. The outer spring has stiffness 40 N/mm and free length 120 mm. The inner spring has stiffness 25 N/mm and free length 105 mm. When a load of 800 N is compressed onto the assembly, determine the force carried by the inner spring.
#26. A Belleville spring washer has an outer diameter of 80 mm, inner diameter of 40 mm, thickness 3 mm, and cone height 2 mm. The spring is made of steel (E = 200 GPa, ν = 0.3). Using the formula P = (4Et⁴)/[(1-ν²)C₁D²] × f(h,t), where C₁ ≈ 0.55, estimate the force required to flatten the spring.
#27. A ball bearing operates under a variable radial load cycle: 10 kN for 40% of time, 6 kN for 35% of time, and 3 kN for 25% of time at a constant speed of 1000 rpm. If the required bearing life is 25,000 hours, determine the required basic dynamic load rating using cubic mean load.
#28. A shaft with a keyway is subjected to a reversed bending moment of 800 N·m and a steady torque of 500 N·m. The shaft diameter is 40 mm, and the fatigue stress concentration factors are Kf = 1.6 for bending and Kfs = 1.4 for torsion. Using the DE-Goodman criterion with Se = 200 MPa and Sut = 550 MPa, determine the factor of safety.
#29. A hydraulic press uses a single-acting cylinder with bore diameter 200 mm and rod diameter 80 mm. The press must exert a force of 500 kN at the tool. If the pump efficiency is 85% and the cylinder mechanical efficiency is 92%, determine the required system pressure.
#30. A tolerance stack-up analysis involves 6 components with bilateral tolerances. The first 3 are critical (±0.03, ±0.04, ±0.05 mm) and the last 3 are non-critical (±0.08, ±0.10, ±0.12 mm). Using the RSS method for critical components and worst-case for non-critical, determine the total assembly tolerance.
#31. A gear train with backlash compensation has a pinion (20 teeth, module 3 mm) driving a gear (60 teeth). The center distance is increased by 0.15 mm from standard. Determine the change in contact ratio if the standard contact ratio is 1.65.
#32. A composite flywheel consists of a steel hub (ρ = 7800 kg/m³) from radius 50 mm to 100 mm and an aluminum rim (ρ = 2700 kg/m³) from radius 100 mm to 200 mm, both 50 mm wide. Determine the kinetic energy stored at 3000 rpm.
#33. A journal bearing has a diameter of 75 mm, length of 60 mm, and radial clearance of 0.05 mm. The shaft rotates at 1500 rpm under a load of 15 kN. If the lubricant viscosity is 0.03 Pa·s, determine the Sommerfeld number.
#34. A leaf spring assembly for a vehicle has 10 leaves, each 75 mm wide and 8 mm thick. The active span is 1200 mm and E = 200 GPa. Using the standard formula with a graduated spring factor of 1.5, determine the load required to produce a 60 mm deflection.
#35. A rotating disc with a central hole (inner radius 30 mm, outer radius 150 mm) is made of steel (ρ = 7800 kg/m³, ν = 0.3). At what angular velocity will the maximum tangential stress at the inner radius reach 200 MPa?
#36. A wire rope with 6×19 construction has a metallic cross-sectional area of 56 mm² and an ultimate tensile strength of 1770 MPa. The rope passes over a sheave with diameter ratio D/d = 20 (d = wire diameter = 0.8 mm). Using the sheave bending stress formula σb = Ed/D, determine the equivalent static tension capacity with a factor of safety of 4.
#37. A brake drum has an inner diameter of 300 mm. A single-pivot internal expanding shoe brake has a lining that subtends an angle of 120° centered at 90° from the pivot. The pivot is at radius 120 mm from the drum center. For a braking torque of 800 N·m with μ = 0.35, determine the required actuating force.
#38. A pressure vessel nozzle reinforcement calculation requires that the area removed by a 100 mm diameter opening in a 15 mm thick shell be compensated. If the nozzle wall thickness is 10 mm and the maximum allowable reinforcement zone extends 2.5 times the shell thickness on each side of the opening, determine the minimum nozzle projection required.
#39. A machine element experiences biaxial fatigue with in-phase loading: σa = 120 MPa, σm = 60 MPa on one axis and τa = 50 MPa, τm = 30 MPa on the other. Using the Sines method with Se = 250 MPa, Sut = 600 MPa, and Sy = 400 MPa, determine the factor of safety.
#40. A chain drive system uses a 60-pitch roller chain. The driver sprocket has 21 teeth rotating at 900 rpm. If the chain velocity variation must not exceed 2%, what is the minimum number of teeth on the driven sprocket?
#41. A cylindrical pressure vessel (ID = 800 mm, t = 20 mm) experiences autofrettage with an overpressure that causes yielding to penetrate to 50% of the wall thickness. If the material has a yield strength of 350 MPa, estimate the residual compressive hoop stress at the inner surface after autofrettage.
#42. A bolted joint uses an M16 bolt with a grip length of 80 mm. The bolt passes through a steel member (30 mm thick) and an aluminum member (50 mm thick). Using E_steel = 200 GPa and E_aluminum = 70 GPa, determine the equivalent joint stiffness.
#43. A shaft coupling uses a rubber bushing with a torsional stiffness of 80,000 N·m/rad. The coupling transmits 25 kW at 1500 rpm. Determine the angular deflection across the coupling.
#44. A helical gear has 30 teeth, normal module 4 mm, and helix angle 20°. The gear operates at 1200 rpm transmitting 15 kW. Determine the axial thrust force on the gear.
#45. A fracture mechanics analysis shows a semi-elliptical surface crack with depth a = 3 mm and half-length c = 8 mm in a plate under tension. The applied stress is 180 MPa. Using the shape factor Q = 1.15 for a/c = 0.375, determine the stress intensity factor at the deepest point.
#46. A reliability analysis considers a standby redundant system with one operating component and one standby. Both have failure rate λ = 0.0005 failures/hour. The switching mechanism has a reliability of 0.95. Determine the system reliability for a mission time of 1000 hours.
#47. A cam-follower system has a translating roller follower. The cam rotates at 600 rpm and the follower has a maximum acceleration of 50 m/s². If the follower mass is 2 kg and the spring preload is 100 N with stiffness 15 N/mm, determine the maximum contact force.
#48. A tapered key with a taper of 1:100 is used in a 50 mm diameter shaft transmitting 600 N·m. The key has a width of 14 mm and length of 80 mm. Determine the maximum extraction force required if the coefficient of friction is 0.15.
#49. A welded T-joint has a 10 mm fillet weld connecting a vertical plate (12 mm thick) to a horizontal plate. The joint is subjected to a bending moment of 2000 N·m about the weld line (200 mm long). Determine the maximum stress in the weld throat including both direct and bending components.
#50. A hollow shaft (OD = 100 mm, ID = 60 mm) is to be replaced by a solid shaft of the same material with equal torsional strength. What diameter is required for the solid shaft?
#51. A machine base is mounted on four identical vibration isolators. The machine mass is 500 kg and the disturbing frequency is 50 Hz. If 90% isolation is required, determine the required stiffness of each isolator.
#52. A gear pump has 12 teeth on each gear with a module of 5 mm. The face width is 30 mm and the pump operates at 1800 rpm. Assuming a volumetric efficiency of 92%, determine the theoretical flow rate.
#53. A press-fit assembly requires a minimum interference of 0.03 mm and maximum interference of 0.08 mm between a 60 mm diameter shaft and hub. Using the ISO fit system, which of the following is the most appropriate designation?
#54. A fatigue specimen is tested under completely reversed loading. After 10⁶ cycles at 250 MPa, the specimen survives. The next load level of 280 MPa causes failure at 2×10⁵ cycles. Using the Basquin equation with b = −0.1, estimate the fatigue strength coefficient σf’.
#55. A worm gear set has a lead angle of 8° and a normal pressure angle of 20°. The coefficient of friction is 0.05. The worm has a pitch diameter of 50 mm and transmits a torque of 150 N·m. Determine the worm gear efficiency.
#56. A column with both ends fixed has a length of 4 m. The column has an I-section with Ixx = 2.5×10⁶ mm⁴ and Iyy = 0.8×10⁶ mm⁴. Determine the critical buckling load for the column (E = 200 GPa).
#57. A structural bolt is subjected to a combined tensile force of 30 kN and shear force of 20 kN. The bolt has a diameter of 16 mm at the shear plane. Determine the von Mises equivalent stress in the bolt shank.
#58. A torsion bar suspension has a diameter of 25 mm and effective length of 1.2 m. The bar is made of steel (G = 79.3 GPa). Determine the angular deflection when supporting a wheel load that produces a torque of 800 N·m.
#59. A thin rectangular plate (400 mm × 300 mm × 5 mm) is subjected to biaxial tension with σx = 100 MPa and σy = 60 MPa. Using E = 200 GPa and ν = 0.3, determine the change in plate thickness.
#60. A contact stress analysis between two parallel cylinders shows the contact width 2b = 3 mm. The cylinders have radii R1 = 50 mm and R2 = 75 mm, and the material has E = 200 GPa and ν = 0.3. Determine the maximum contact pressure.
#61. A band brake with a wrap angle of 270° uses a steel band 2 mm thick and 60 mm wide. The drum diameter is 400 mm and rotates at 200 rpm. If the coefficient of friction is 0.28 and the maximum band tension is 4000 N, determine the braking power.
#62. A precision ball screw has a lead of 10 mm and a ball diameter of 5 mm. The screw supports an axial load of 8 kN with a coefficient of friction of 0.004 (due to ball contact). Determine the driving torque required.
#63. A two-stage gear reducer has an overall ratio of 20:1. Stage 1 is a helical gear set (ratio 4:1) and Stage 2 is a spur gear set (ratio 5:1). The input power is 15 kW at 1500 rpm. If Stage 1 efficiency is 97% and Stage 2 efficiency is 98%, determine the output torque.
#64. A hydraulic cylinder with cushioning at end of stroke has a bore of 80 mm and cushion plunger diameter of 25 mm. The piston velocity is 0.3 m/s and the piston plus load mass is 100 kg. If the cushion length is 30 mm, determine the peak cushion pressure.
#65. A surface hardened shaft has a case depth of 2 mm on a 40 mm diameter shaft. The case material has a yield strength of 800 MPa and the core has 400 MPa. When subjected to a bending moment, determine the ratio of the maximum allowable bending moment compared to a uniform shaft of core material only.
#66. A snap ring retains a component under an axial load of 5 kN. The ring has an outer diameter of 50 mm when installed, thickness 2.5 mm, and width 3 mm. The ring material has a yield strength of 1200 MPa. Determine the factor of safety against shear failure in the ring.
#67. A disc spring stack has 3 springs in parallel and 2 such parallel groups in series. Each individual spring has stiffness 500 N/mm and can deflect 1 mm before going flat. Determine the maximum force the stack can support at full deflection.
#68. A timing belt drive uses an HTD 8M pitch belt. The driver pulley has 24 teeth and rotates at 1800 rpm. The driven pulley has 72 teeth. If the belt width is 30 mm and the allowable tension per mm width is 12 N/mm, determine the maximum power that can be transmitted.
#69. A creep analysis of a turbine blade at 850°C shows a steady-state creep rate of 2×10⁻⁸ per hour under 150 MPa stress. Using the Norton creep law with exponent n = 4, estimate the creep rate at 180 MPa under the same conditions.
#70. A mechanical seal face has an inner diameter of 40 mm and outer diameter of 55 mm. The spring load is 800 N and the sealed pressure is 1.5 MPa acting on the outer half of the face. If the balance ratio is 0.75, determine the face contact pressure.
#71. A shock absorber uses a damping coefficient c = 3000 N·s/m with a spring k = 50 kN/m. The system mass is 200 kg. Determine the damping ratio and classify the system response.
#72. A beam column with a rectangular section (60 mm × 80 mm) and length 1.5 m is subjected to an axial compressive load of 50 kN and a transverse load of 3 kN at mid-span. The column has pinned ends. Using the secant formula approach, estimate the maximum compressive stress (E = 200 GPa).
#73. A gasketed joint requires a gasket seating stress of 25 MPa minimum. The gasket has an inner diameter of 200 mm, outer diameter of 250 mm, and the bolt circle has 12 M12 bolts (At = 84.3 mm²). Determine the required bolt stress to achieve proper gasket seating.
#74. A pneumatic cylinder with bore 50 mm operates at 0.6 MPa gauge pressure. The cylinder is used in a pick-and-place application with 30 cycles per minute. If the stroke is 150 mm and the load mass is 5 kg, determine the minimum cycle time limited by acceleration (assume max acceleration = 3g).
#75. A high-speed spindle bearing arrangement uses preloaded angular contact bearings in back-to-back configuration. Each bearing has a dynamic load rating of 25 kN. The spindle operates at 15,000 rpm with a radial load of 1.5 kN and axial preload of 500 N. Estimate the L10 life of the bearing set.
#76. A shot peening process introduces residual compressive stress to a depth of 0.3 mm with a maximum value of -350 MPa at the surface, decreasing linearly to zero. If the component experiences a bending stress that varies from +200 MPa to -100 MPa at the surface, determine the effective stress range for fatigue analysis.
#77. A universal joint (Cardan joint) transmits power between shafts at an angle of 25°. The input shaft rotates at a constant 1000 rpm. Determine the maximum and minimum output shaft velocities during one revolution.
#78. A thread stripping calculation for an M20×2.5 bolt in a cast iron (lower strength) housing requires minimum engagement. If the bolt material has tensile strength 800 MPa and the housing material has shear strength 180 MPa, and the thread stripping area factor is 0.9×π×d×Le, determine the minimum engagement length.
#79. A rolling element bearing operates with oil film lubrication. The specific film thickness λ = 2.5 (mixed lubrication regime). If the composite surface roughness is 0.4 µm, determine the minimum oil film thickness.
#80. A centrifugal clutch has 4 shoes, each with mass 0.5 kg at a radius of 75 mm from the center. The friction surface is at 100 mm radius with μ = 0.35. The spring preload holds the shoes against the hub until the engagement speed of 800 rpm. Determine the torque capacity at 1500 rpm.
#81. A GD&T position callout specifies Ø0.5 MMC for a Ø12.0 +0.1/-0 hole pattern of 4 holes. The holes are produced at actual sizes of 12.02, 12.05, 12.08, and 12.03 mm. For the hole measuring 12.08 mm, what is the total allowable position tolerance?
#82. A thermal stress analysis of a thick-walled cylinder shows the inner surface at 400°C and outer surface at 100°C under steady-state conditions. If E = 200 GPa, α = 12×10⁻⁶/°C, ν = 0.3, and the temperature distribution is logarithmic, estimate the maximum thermal stress at the inner surface for ri = 50 mm and ro = 100 mm.
#83. A weldment design uses a combination of fillet and groove welds. A T-joint has a partial penetration groove weld (effective throat 8 mm) plus a reinforcing fillet weld (leg 6 mm) on each side. The weld length is 200 mm and the joint must carry 180 kN perpendicular to the weld axis. Determine the average stress across all weld throats.
#84. A lever system uses a pivot pin of 12 mm diameter in a bronze bushing. The lever applies a 2 kN force at 200 mm from the pivot. The bushing has a length of 20 mm and allowable bearing pressure of 15 MPa. Determine if the bearing stress exceeds the allowable and by how much (expressed as a percentage).
#85. A fatigue crack growth analysis uses the Paris law da/dN = C(ΔK)^m with C = 1×10⁻¹² and m = 3 (units: mm/cycle, MPa√m). An edge crack grows from 2 mm to 10 mm under a stress range of 150 MPa. Using Y = 1.12 and numerical integration, estimate the number of cycles to grow through this range.
#86. A machine tool spindle is designed for maximum rigidity. A solid shaft of diameter D and a hollow shaft with OD = 1.2D and wall thickness t are being compared. For equal torsional rigidity, what should be the ratio t/D?
#87. A conical compression spring has a large end mean diameter of 60 mm, small end mean diameter of 30 mm, wire diameter of 5 mm, and 8 active coils (G = 79.3 GPa). Estimate the spring rate using the average diameter approach.
#88. A rotating shaft experiences critical speed resonance. The shaft has a uniform cross-section with I = 4×10⁵ mm⁴, E = 200 GPa, length 600 mm, and supports a 10 kg disk at its center. Using the Rayleigh method, estimate the first critical speed.
#89. A hypoid gear set has an offset of 40 mm, pinion pitch diameter of 60 mm, and gear pitch diameter of 200 mm. The pinion rotates at 3000 rpm transmitting 8 kW. If the efficiency is 92%, determine the output torque.
#90. A Hertzian contact analysis between a sphere (R = 25 mm) and a flat plate shows a contact radius of 1.2 mm under a force F. Both parts are steel (E = 200 GPa, ν = 0.3). Determine the applied force.
#91. A welded steel frame joint uses complete penetration welds. The joint connects a 150×100×10 mm rectangular tube to a baseplate. The tube carries an axial load of 200 kN and a moment of 8 kN·m about the weak axis. Determine the maximum weld stress.
#92. A pneumatic control valve uses a diaphragm actuator with effective diameter 150 mm operating against a spring. The spring rate is 25 N/mm and provides 800 N initial force. If the control pressure range is 0.02 to 0.1 MPa, determine the valve stem travel.
#93. A synchronous belt drive uses an 8M pitch belt with 40-tooth driver at 1200 rpm and 80-tooth driven pulley. The belt width is 25 mm with allowable tension of 15 N/mm width. The center distance is 350 mm. Calculate the maximum transmissible power.
#94. A biaxial stress state in a thin plate has σ₁ = 180 MPa and σ₂ = 90 MPa. The plate thickness is 8 mm. Using the Tresca criterion, determine the minimum thickness required if the yield strength is 300 MPa and a factor of safety of 2 is required.
#95. A preloaded bolt group of 8 M16 bolts (At = 157 mm² each) on a 200 mm bolt circle is subjected to an overturning moment of 15 kN·m in addition to a tensile load of 40 kN. Determine the maximum tensile stress in the most heavily loaded bolt.
#96. A shaft with shoulder fillet (D = 60 mm, d = 45 mm, r = 4 mm) transmits 25 kW at 500 rpm. The theoretical stress concentration for bending Kt = 1.7 and for torsion Kts = 1.35. Using notch sensitivity q = 0.8 for both, determine the maximum equivalent stress using DE-Elliptic criterion.
#97. A corrugated flexible coupling allows 2° angular misalignment and 1.5 mm parallel misalignment. The coupling connects shafts of 50 mm diameter operating at 1500 rpm. If the coupling has torsional stiffness of 50,000 N·m/rad and transmits 30 kW, determine the reaction moment due to angular misalignment.
#98. A cumulative fatigue damage analysis considers a component with endurance limit 280 MPa subjected to spectrum loading. Block 1: 5000 cycles at 350 MPa (Nf=50,000), Block 2: 15000 cycles at 300 MPa (Nf=200,000), Block 3: 100000 cycles at 260 MPa (Nf=10⁶). Estimate remaining life fraction.
#99. A valve stem seal experiences a combination of internal pressure (3 MPa) and packing gland load. The stem diameter is 25 mm, seal length is 20 mm, and the coefficient of friction is 0.12. If the packing radial pressure is 8 MPa, determine the stem extraction force.
#100. A worm-wheel gear set operates with a worm lead angle of 12° and normal pressure angle of 20°. The coefficient of friction is 0.045. Using the virtual coefficient formula for an ACME thread, determine the actual drive efficiency when power flows from worm to wheel.
