Engineering mechanics covers a wide range of problems, from determining the forces acting on a stationary component to calculating stresses, deformation, buckling and the motion of machines.
The first step is normally to identify what type of engineering problem you are trying to solve. This guide helps select the appropriate RoyMech reference for the problem rather than reproducing the detailed equations, tables and derivations contained on those pages.
| Engineering Question | Start Here |
|---|---|
| I need to resolve forces into components or work with force directions. | Vectors |
| I need reactions, forces or moments in a stationary structure or component. | Statics |
| I know how something moves but I am not yet considering the forces causing the motion. | Kinematics |
| I need to relate force, mass, acceleration, momentum or energy to motion. | Dynamics and Kinetics |
| I need to analyse a four-bar or other mechanical linkage. | Mechanical Linkages |
| I need mechanical advantage, velocity ratio or efficiency for a simple machine. | Simple Machines |
| I need to identify whether a component is in tension, compression, shear, bending or torsion. | Component Loading |
| I need basic elastic stress, strain, Young's modulus, Poisson's ratio or shear modulus. | Stress and Strain |
| I have combined stresses and need to assess yielding or failure. | Yield and Failure Criteria |
| I need principal stresses or maximum shear stress from a plane-stress state. | Mohr's Circle |
| I have a slender member in compression and need to check buckling. | Column and Strut Buckling |
| I need stresses in a thick pressure cylinder or an interference fit. | Thick-Walled Cylinders |
| I need stresses in a high-speed rotating disc or cylinder. | Rotating Discs and Cylinders |
| I need shear stress or angular twist caused by torque. | Torsion |
| I need yield strength, proof strength, UTS, ductility or tensile-test behaviour. | Stress-Strain Curve |
| I need stress or deflection in a thin circular, rectangular or annular plate. | Loaded Flat Plates |
A useful first distinction in mechanics is whether the problem concerns forces in equilibrium, motion itself, or the forces producing motion.
Use Engineering Statics when the component or system is being treated as being in equilibrium.
Typical problems include:
Statics is often the first stage of a stress calculation. The external forces and reactions are determined first, after which the resulting component loading and stresses can be calculated.
Use Kinematics when the main question is how something moves rather than what forces cause the motion.
Typical quantities include:
Use Dynamics and Kinetics when forces, moments, mass or inertia must be related to acceleration and motion.
This includes problems involving:
Many statics and dynamics calculations depend on vector operations. Use Vectors in Engineering Mechanics for vector components, addition, scalar and vector products, force directions and related vector operations.
Mechanism problems can involve either the selection of a mechanism or the detailed kinematic analysis of a linkage.
If you are deciding how to produce a particular type of motion, start with the:
Mechanism Help and Selection Guide
That guide covers mechanisms for reciprocating, rocking, intermittent, indexing and one-way motion, including ratchets, escapements, cams and linkages.
If the mechanism has already been selected and you need to analyse a four-bar linkage, mobility, Grashof condition, mechanical advantage, velocity or acceleration, use:
Mechanical Linkages – Four-Bar Mechanisms and Kinematic Analysis
Use Simple Machines when the problem concerns mechanical advantage, velocity ratio or ideal efficiency in arrangements such as:
For the detailed engineering design of screws transmitting substantial axial load or power, use the RoyMech Power Screw references instead.
If the load is known but you are unsure which stress calculation applies, start with:
Component Loading – Stress, Strain and Loading Conditions
The principal loading modes are:
| Loading | Typical Effect | Common Next Step |
|---|---|---|
| Tension | Normal tensile stress and extension | Stress and Strain |
| Compression | Normal compressive stress and shortening | Stress and Strain |
| Shear | Shear stress and shear deformation | Stress and Strain |
| Bending | Normal bending stress and deflection | Beam Calculations |
| Torsion | Shear stress and angular twist | Torsion |
| Combined loading | Multiaxial stress state | Mohr's Circle / Yield and Failure Criteria |
These terms are closely related but answer different engineering questions.
Use Stress and Strain – Basic Elastic Theory when you need relationships involving:
Use the Stress-Strain Curve reference when the question concerns properties obtained from a tensile test, including:
Components are often subjected to more than one stress component at the same time. A shaft, for example, may experience bending stress and torsional shear stress simultaneously.
Use Mohr's Circle to transform a plane stress state and determine:
Use Yield and Failure Criteria when the stress state must be compared with material strength.
The page covers:
For ductile metals under multiaxial static loading, Tresca and von Mises are commonly encountered yield criteria. Material behaviour, loading conditions and the applicable design standard should determine which criterion is used.
A compression member does not necessarily fail by simple compressive yielding. A sufficiently slender member may become unstable and buckle at a much lower load.
Use:
Column and Strut Buckling – Euler, Rankine and Perry-Robertson
for:
Pressure-loaded components require different treatment depending on their geometry and wall thickness.
Use Thick-Walled Cylinders where radial stress cannot reasonably be neglected through the wall thickness.
The reference covers:
Do not confuse a pressure-stress calculation with an external-pressure buckling calculation. A cylinder can become unstable under external pressure even when an elastic stress calculation alone appears acceptable.
Rotation creates body forces throughout the material. At sufficiently high speed these can produce important radial and circumferential stresses even when no external mechanical load is applied.
Use:
Rotating Discs and Cylinders – Radial and Hoop Stresses
for:
These calculations can be relevant to flywheels, rotors, high-speed discs and other rotating machinery.
Torque produces torsional deformation and generally creates shear stress. For circular shafts, the familiar elastic torsion relationship is:
Use the RoyMech:
for shaft torsion, torsional section properties and the associated torsion references.
A flat plate carrying transverse load behaves differently from a beam because the load can be carried by bending in two directions.
Use:
Loaded Flat Plates – Stress and Deflection
for preliminary elastic calculations involving:
The RoyMech plate equations are based on thin-plate, small-deflection assumptions. If deflection becomes significant relative to plate thickness, membrane action and geometric nonlinearity may become important.
These are frequently confused when first approaching a structural mechanics problem.
| Component Behaviour | Usually Start With |
|---|---|
| A long member carrying transverse loads, with bending predominantly about one axis. | Beam Analysis |
| A broad thin surface carrying transverse load and bending significantly in two directions. | Plate Analysis |
| A slender member carrying axial compression where instability may govern. | Column / Strut Buckling |
| A short member primarily carrying axial load without an instability problem. | Component Loading and Stress and Strain |
Many practical engineering calculations follow approximately this sequence:
A calculated stress below yield strength does not automatically mean that a component is satisfactory.
Depending on the application, also consider:
The appropriate checks depend on the component, material, operating environment and consequences of failure.
Engineering equations describe an idealised model of a real component. Before using a result, check that the assumptions behind the calculation are reasonable for the actual geometry, material, loading and supports.
A calculation can be mathematically correct and still be the wrong calculation for the engineering problem. Selecting the correct model is therefore just as important as evaluating the equation correctly.
Where a recognised design standard governs the component or application, the standard should take precedence over a general reference calculation, particularly where safety factors, load combinations, material limits, fatigue, instability or inspection requirements are specified.
Experienced engineers who already know the required method can go directly to the RoyMech Mechanics reference pages: