Solver catalogue

Resultant of Concurrent Forces

Add concurrent 2D forces to find resultant magnitude, direction, components, and the equilibrant. Follow the vector calculations step by step.

Particle Equilibrium (Cable Tensions)

Find one or two unknown cable or member forces at a point using horizontal and vertical equilibrium, with worked steps and sign conventions.

Moment of Forces About a Point

Calculate the moment of 2D forces and applied couples about a point. See each contribution, the total moment, and the resultant force.

Friction on an Incline

Find normal force, available friction, and the force needed to move a block on an incline. Compare static and kinetic friction with worked steps.

Normal, Shear & Bearing Stress

Calculate average normal stress, bolt or pin shear stress, and plate bearing stress. Check factors of safety against the allowable stresses you enter.

Thermal Stress (Constrained Bar)

Calculate expansion, stress, and restraint force for a bar between rigid supports, including an initial gap and a uniform temperature change.

Thin-Walled Pressure Vessel

Find hoop and longitudinal stress in thin-walled cylinders or stress in spheres. Calculate required thickness from a given allowable stress.

Beam Support Reactions

Find support reactions for simply supported beams and cantilevers under point loads, distributed loads, and moments, with equilibrium steps.

Beam Shear & Moment Diagrams

Calculate beam reactions and shear force and bending moment diagrams. Find maximum values and their locations for supported single-span beams.

Beam Deflection by Superposition

Calculate beam deflection and slope for standard simply supported and cantilever load cases. Combine closed-form solutions and find peak deflection.

Beam Deflection by Double Integration

Find beam deflection and slope by double integration, including partial distributed loads and overhangs. See the elastic curve and peak deflection.

Composite Section Properties

Find area, centroid, moments of inertia, and radii of gyration for composite sections made from simple shapes, including holes, with worked steps.

Axially Loaded Stepped Bar

Find internal force, normal stress, and elongation in a stepped or composite bar fixed at one end, with axial loads and optional temperature change.

Torsion of Circular Shafts

Calculate shear stress and angle of twist for solid or hollow circular shafts under torque, or derive torque from transmitted power and speed.

Euler Column Buckling

Calculate Euler critical buckling load for an ideal elastic column. Compare end conditions, weak-axis stiffness, slenderness, and critical stress.

Mohr's Circle / Stress Transformation

Find principal stresses, maximum shear stress, and plane angles for a 2D stress state. Transform stresses at a chosen angle with worked steps.

Truss Analysis (Method of Joints)

Find reactions and member forces in a determinate plane truss. Follow joint equilibrium and identify tension, compression, and zero-force members.

Fluid Properties (ρ, γ, SG)

Convert fluid density, unit weight, and specific gravity. Also find the mass and weight of a volume or the pressure at a given depth.

Buoyancy & Archimedes' Principle

Calculate buoyant force, submerged fraction, or apparent weight. Use Archimedes' principle to find an object's volume and specific gravity.

Hydrostatic Pressure & Manometers

Calculate pressure through a series of static fluid columns. Follow each manometer leg and find the final gauge and absolute pressure.

Hydrostatic Force on a Submerged Surface

Find the hydrostatic force and center of pressure on a fully submerged rectangular, circular, or triangular plane, vertical or inclined.

Continuity (Flow Between Pipe Sections)

Use Q = AV to find missing flow rates, velocities, or areas between pipe sections for incompressible flow, with unit conversions and worked steps.

Energy Equation (Bernoulli with Machines & Losses)

Solve the energy equation between two flow sections for one unknown, including pressure, velocity, pump head, head loss, elevation, or pump power.

Darcy–Weisbach Pipe Head Loss

Find pipe head loss, flow rate, or diameter using Darcy-Weisbach. Include minor losses and see friction factor, Reynolds number, and flow regime.

Hazen–Williams Pipe Flow

Calculate head loss, flow rate, or required diameter for a full circular water pipe using Hazen-Williams, with SI or US units and worked steps.

Manning Normal Depth

Find normal depth in rectangular, trapezoidal, triangular, or partly full circular channels. See velocity, hydraulic radius, and Froude number.

Critical Depth & Froude Number

Calculate open-channel critical depth and Froude number for common cross-sections. Identify subcritical or supercritical flow at a given depth.

Rational Method Peak Flow

Estimate peak stormwater runoff using Q = CiA for a small catchment. Combine runoff coefficients across subareas and follow the unit conversions.

Runoff Depth & φ-Index

Calculate runoff depth, runoff coefficient, total abstractions, and the phi-index for a uniform storm using rainfall and watershed runoff data.

Horizontal Circular Curve Geometry

Find tangent length, arc length, chord, offsets, and PC/PT stations for a simple circular curve from its central angle and radius or degree of curve.

Minimum Curve Radius (Superelevation)

Calculate horizontal curve radius from design speed, superelevation, and side friction. Follow the equation in SI or US units for coursework.

Greenshields Traffic Flow

Relate traffic speed, density, and flow with the Greenshields model. Find capacity and compare congested and uncongested density solutions.

Vertical Curve Elevations (Symmetric Parabola)

Calculate elevations and stations on a symmetric parabolic vertical curve. Find BVC/EVC, K value, and any high or low point within the curve.

Stopping Sight Distance (AASHTO)

Calculate reaction and braking distance with road grade adjustment. See computed stopping sight distance and the rounded AASHTO-based value.

Passing Sight Distance (AASHTO 2011+)

Look up and interpolate AASHTO 2011+ passing sight distances for two-lane highways. See the assumed passing and passed vehicle speeds.

Soil Phase Relationships

Find void ratio, porosity, water content, saturation, and soil unit weights from a sufficient set of known values, with a worked phase table.

USCS Soil Classification (ASTM D2487)

Classify inorganic soil from gradation and Atterberg limits using the USCS flowchart. Follow the steps to a group symbol and soil name.

AASHTO Soil Classification (M 145)

Find the AASHTO soil group and group index from sieve passing percentages, liquid limit, and plasticity index, with classification steps.

Vertical Effective Stress Profile

Calculate total stress, pore water pressure, and effective stress with depth in layered soil. Set the water table and view the stress profile.

Darcy Seepage Velocity & Discharge

Use Darcy's law to find discharge velocity, volumetric flow, and true seepage velocity from hydraulic conductivity, gradient, area, and porosity.

Triaxial Test — Effective Friction Angle

Interpret a triaxial test at failure to find effective principal stresses and friction angle from a given cohesion, plus the failure-plane angle.

Terzaghi Bearing Capacity

Calculate ultimate and gross allowable bearing capacity for shallow footings using supplied Terzaghi factors, footing shape, and factor of safety.

Stream Mixing & Dilution

Find mixed flow, concentration, and mass loading for steady-state stream mixing. Optionally include completely mixed first-order decay.

Tank Fill / Detention Time

Calculate tank filling or detention time, required volume, or flow rate using t = V/Q, including constant simultaneous inflow and outflow.

Sedimentation Tank (Overflow Rate)

Calculate clarifier surface overflow rate, detention time, weir loading, and flow-through velocity from tank dimensions and flow rate.

BOD (Dilution Method)

Calculate biochemical oxygen demand from dissolved oxygen readings and bottle dilution. Check oxygen depletion and residual validity limits.

Compound-Interest Factors (Time Value of Money)

Calculate the eight standard engineering economy interest factors, convert nominal to effective rates, and apply a factor to a given amount.

Present / Annual / Future Worth Comparison

Compare alternatives by present, annual, or future worth at a given MARR. Enter signed cash flows, uniform series, and salvage values.

Internal Rate of Return (IRR)

Find internal rates of return for signed cash flows within a bounded search range. Follow the calculation and compare NPV at a given MARR.

Particle Kinematics

Solve constant-acceleration motion or projectile flight. Find missing velocities, distance, time, range, or peak height with worked steps.

Work–Energy Theorem

Find speed or travel distance using work and kinetic energy for a particle, including constant forces, gravity, springs, and kinetic friction.

Impulse–Momentum & 1-D Collisions

Solve force-time impulse problems or direct 1D collisions. Find velocities, impulse, and kinetic energy loss with conservation equations.

Descriptive Statistics

Calculate mean, median, mode, quartiles, and sample or population variance and standard deviation for a list of values, with worked steps.

Linear Regression (Least Squares)

Fit a least-squares line and find slope, intercept, correlation, R-squared, and standard error. Make predictions at chosen x values.