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Open CalculatorAll Mechanical: Machine Design and Materials PE Equations (19)
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Axial Stress
Normal stress due to axial load.
basicHigh Frequency -
Bearing Life
L10 life for ball bearings.
intermediate -
Belt Tension Ratio
Ratio of tight to slack side tensions.
intermediate -
Bending Stress
Normal stress due to bending moment.
basicHigh Frequency -
Bolt Preload
Initial tension in bolted joint.
intermediate -
Euler Buckling Load
Critical load for column buckling.
intermediateHigh Frequency -
Factor of Safety
Ratio of strength to stress.
basicHigh Frequency -
Gear Ratio
Ratio of input to output speed.
basicHigh Frequency -
Goodman Equation for Fatigue
Modified Goodman criterion for fluctuating stresses.
intermediateHigh Frequency -
Hoop Stress in Pressure Vessel
Circumferential stress in thin-walled vessel.
intermediateHigh Frequency -
Hydraulic Cylinder Force
Force output of cylinder.
basicHigh Frequency -
Interference Fit Stress
Contact pressure in interference fit.
intermediate -
Principal Stresses from Mohr's Circle
Maximum and minimum normal stresses.
intermediateHigh Frequency -
Natural Frequency of Single DOF System
Undamped natural frequency.
basicHigh Frequency -
Shear Stress
Average shear stress.
basicHigh Frequency -
Helical Spring Rate
Stiffness of compression spring.
intermediate -
Thermal Stress
Stress due to temperature change in constrained member.
basicHigh Frequency -
Torsional Shear Stress
Shear stress due to torque.
intermediateHigh Frequency -
Weld Strength
Shear stress in fillet weld.
basicHigh Frequency
Frequently Asked Questions
How do I use Axial Stress on the PE exam?
Remember that axial stress is positive for tension and negative for compression. Always check if the cross-sectional area is given or needs to be calculated from diameter/dimensions. Watch units carefully - stress problems often mix kips with inches or kN with mm.
How do I use Bearing Life on the PE exam?
L10 life represents 90% reliability (10% of bearings fail by this point). Always verify units match between C and P. For exam problems, you may need to calculate equivalent load P from radial and axial components using bearing-specific factors.
How do I use Belt Tension Ratio on the PE exam?
This is the Eytelwein (belt friction) equation. Remember wrap angle must be in radians. Larger wrap angles and higher friction coefficients allow greater tension ratios before slipping. Often appears with power transmission problems where you need to check if belt will slip under load.
How do I use Bending Stress on the PE exam?
This is THE fundamental bending equation. Know that y is measured from the neutral axis (centroid), maximum stress occurs at extreme fibers (y = c), and the equation assumes linear elastic behavior. Watch for section modulus S = I/c shortcuts.
How do I use Bolt Preload on the PE exam?
CRITICAL: Torque coefficient definitions vary. Some sources use K where T = K×F_i (K ≈ 0.2), others use K_t where F_i = K_t×T (K_t ≈ 5). Always check the problem statement for the relationship direction. Standard lubricated bolts: K ≈ 0.2, so F_i ≈ T/0.2 = 5T.