In-depth guides on structural analysis, geotechnics, hydrology, construction, statistics and AI for engineers, written for students and working professionals.
Four equations describe every classical electric and magnetic phenomenon, from a compass needle to Wi-Fi to sunlight. This guide states each law in integral and differential form, explains what it means physically with an example,
Every power station, transformer, electric guitar pickup and wireless charger works because a changing magnetic flux induces a voltage. This guide explains magnetic flux, Faraday's law, the direction rule of Lenz's law, motional EMF, the AC generator, transformers, inductance and eddy currents, with worked examples and an animated generator you can control.
Infiltration decides how much rain becomes runoff. This guide explains the three classic infiltration models, gives the Rawls Green-Ampt parameters for all 11 soil textures, shows how to compute ponding time, and works through the φ-index and W-index.
The FAO-56 Penman-Monteith equation is the international standard for reference evapotranspiration. This guide explains every term, walks through all twelve calculation steps, reproduces the official FAO worked example (ET₀ = 3.9 mm/day),
Rain gauges measure rainfall at points, but floods, water budgets and hydrological models need the average over an area. This guide explains the three classical methods, lets you drag gauges on a live catchment and watch the Thiessen polygons
The rational method is the most widely used way to size storm drains, culverts and gutters for small catchments. This guide covers the formula in SI and US units, where each term comes from, how to pick C, how to compute the time of concentration and
A hydrograph is a graphical representation of the variation of discharge (or stage) of a stream at a given gauging station plotted against time. In hydrology, it is the single most important tool for understanding and quantifying the rainfall-runoff response of a catchment. Every flood estimate, reservoir design, culvert sizing, and floodplain mapping exercise depends either directly on a measured hydrograph or on a model capable of reproducing one.
The 3-point bending test (also written as three-point bend test or flexure test) is a standardised mechanical test that measures the flexural properties of a material by loading a beam specimen at its midpoint while it rests on two supports
he complete reference for the Hollomon power law
: derivation, physical meaning of K and n, true-vs-engineering stress-strain conversion, worked examples for annealed copper and structural steel, comprehensive K and n table for 20+
A complete reference covering the normal distribution formula, the 68-95-99.7 empirical rule, Z-scores and probability tables, skewness, kurtosis, real-world examples across engineering, biology, finance, and education - plus an interactive calculator.
The displacement method (also called the stiffness method or equilibrium method) is the second fundamental approach to analysing statically indeterminate structures. Instead of treating unknown forces as primary unknowns, the displacement method takes joint displacements and rotations as unknowns and enforces equilibrium at every free joint.
The force method, also called the compatibility method, flexibility method, or method of consistent deformations, is a classical technique for analysing statically indeterminate structures. It was developed......
In the realm of artificial neural networks (ANNs), the loss function serves as a critical component that guides the training process. It quantifies the difference between the model's predictions and the actual target values, enabling optimization algorithms to adjust the network's parameters for better performance.
This paper, “Knowledge-informed deep learning for hydrological model calibration: an application to Coal Creek Watershed in Colorado,” mainly focuses on improving the efficiency and reducing the computational load in hydrological model calibration...
Discover the structural behaviour and how retaining walls transform landscapes, from choosing materials to planning installation, maintenance, and creative landscaping.
Compute the magnetic flux density B produced by steady currents in the six most common conductor shapes, using the Biot–Savart law and Ampère's law. The calculator gives B in tesla, millitesla, microtesla and gauss, plots the field along the axis, maps the exact off-axis field of a loop, compares finite and ideal solenoids, and shows the substituted formula for every result.
Place up to eight point charges, drag them around, and watch the electric field lines and equipotential lines update live. Move the probe to read the electric field vector and potential at any point, see the net Coulomb force on every charge, or use the quick Coulomb's law calculator for two charges in any medium.
Paste a monthly rainfall series and get the SPI at 1 to 24 months using the standard McKee et al. (1993) gamma method, the drought category of every month, a list of drought events with duration and severity, and a multi-scale heatmap that shows how short dry spells grow into long droughts.
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