Engineering Analysis,
Made Clear.
Advanced beam analysis, reaction forces, shear & bending diagrams, and step-by-step mathematical solutions — built for engineering students and structural engineers.
∑F_y = 0 ⟹ R_A + R_B - P = 0
∑M_A = 0 ⟹ R_B(10) - (50)(5) = 0
⟹ R_B = 25.00 kN, R_A = 25.00 kN
Meet Beam Master
Analytical and stiffness-based beam analysis with step-by-step solutions. Visualize shear and bending moment diagrams, calculate elastic deflection, and understand every step of the derivation.
Exact SFD & BMD Curves
Instant shear jump calculations, point moments, and continuous bending moment diagrams.
Multiple Boundary Conditions
Pin, roller, fixed, free, and internal hinge supports for determinate and indeterminate spans.
Deflection & Slope Profiles
Double integration and Macaulay singularity solving with elastic modulus E and moment of inertia I.
Step-by-Step LaTeX Derivations
Transparent 11-step mathematical walkthroughs showing equilibrium equations and boundary values.
High-Resolution PDF Reports
Generate engineering-ready calculation sheets with vector diagrams and project metadata.
Project Cloud Sync
Store, duplicate, and share beam setups with fast one-click library access.
M(x) = R_A⟨x⟩¹ - P⟨x - a⟩¹ - ½w⟨x - c⟩² + M₀⟨x - d⟩⁰
EI · v(x) = ⅙R_A⟨x⟩³ - ⅙P⟨x - a⟩³ - ¹⁄₂₄w⟨x - c⟩⁴ + C₁x + C₂
Real Engineering Solvers. Verified Accuracy.
Our purpose-built engineering platform spans structural mechanics, stress transformations, section properties, and thermodynamics — backed by thousands of regression tests and benchmarked proofs.
Beam Master
1D Continuous Beam & Deflection Solver
Analytical and stiffness-based continuous beam solver with 414/414 passing tests. Handles angled loads, internal hinges, piecewise cut sections, and 11-step LaTeX derivations.
Mohr Master
Plane Stress & Mohr's Circle Calculator
Interactive 2D plane stress transformation engine. Calculates principal stresses (σ₁, σ₂), maximum in-plane shear (τ_max), and synchronizes rotating stress elements in real time.
Truss Master
2D Planar Truss Analysis Platform
Hybrid 2D truss engine combining a 100% accurate global stiffness matrix backend with step-by-step Method of Joints and Method of Sections derivations.
Section Properties (ZED 2)
Exact Green's Theorem Geometric Engine
Clean-room cross-section calculator using Green's theorem and Kahan compensated summation. Verified to 10⁻⁹ precision on primitive geometry and 10⁻⁶ off-origin.
ThermoCore
Tiered Thermodynamics & Cycle Engine
High-performance thermodynamics backend powered by CoolProp 7.2.0 with 88/88 benchmarked problems across state properties, energy balances, Rankine/Brayton cycles, and transient CVs.
From Problem to Engineering Solution
A clear four-step process built to deepen conceptual understanding and ensure calculation accuracy.
Define
Enter span length, support types, material modulus (E), cross-section inertia (I), and load positions (Point, UDL, Moment).
Analyze
Our deterministic analytical engine calculates equilibrium reactions, shear equations, and Macaulay polynomials instantly.
Visualize
Inspect interactive, high-precision Shear Force (SFD), Bending Moment (BMD), and elastic Deflection diagrams in real time.
Understand
Review complete 11-step mathematical derivations with LaTeX formatted equations, boundary conditions, and printable PDF exports.
Why Engineers Trust AskOnlineTutor
Built by engineers for students, educators, and practicing professionals who demand mathematical accuracy and transparent derivations.
Deterministic Mathematical Rigor
Never approximate black-box answers. From 414/414 verified beam tests to Green’s theorem evaluated to 10⁻⁹ precision with Kahan summation, every calculation is mathematically grounded.
Transparent Step-by-Step Proofs
See every equilibrium resolution, singularity integral, stress rotation, and cycle energy balance in LaTeX formulas with actual numerical substitutions and physical interpretations.
Ecosystem of Specialized Solvers
Integrated suite spanning Continuous Beams (Beam Master), Plane Stress (Mohr Master), 2D Trusses (Truss Master), Exact Cross-Sections (ZED 2), and Thermodynamics (ThermoCore).
Verified Against Benchmark Datasets
Calibrated against standard engineering textbooks (Beer & Johnston, Hibbeler, Moran & Shapiro) and independently audited with automated regression suites.
Designed for Every Stage of Engineering
Understand the calculation, not just the answer.
Master statics, mechanics of materials, and structural analysis with transparent mathematical derivations and interactive diagrams.
Free Calculators & Engineering Guides
Strengthen your theoretical foundations with verified structural formulas and interactive calculation tools.
Interactive Calculators
Beam Calculator
General beam solver for point loads, UDL, and overhangs.
Cantilever Beam Calculator
Fixed-end cantilever analysis for point loads and uniform distributed loads.
Simply Supported Beam Calculator
Pinned-roller span with midspan deflection and peak bending moments.
Bending Moment Diagram (BMD)
Inflection points, zero-shear crossings, and peak bending moments.
Shear Force Diagram (SFD)
Shear jump discontinuities, distributed load slopes, and reaction shears.
Beam Deflection Calculator
Elastic curve deflection v(x) via double integration & Macaulay method.
Technical Articles & Guides
How to Draw Shear Force Diagrams
Equilibrium equations, sign conventions, and shear force jumps.
How to Draw Bending Moment Diagrams
Constructing BMD from SFD curves and locating maximum moments.
Macaulay’s Method for Beam Deflection
Singularity functions, double integration, and evaluating constants.
Moment of Inertia & Parallel Axis Theorem
Second moment of area, centroid determination, and flexural rigidity.
Start Building Better Engineering Solutions Today.
Explore Beam Master today and discover a growing suite of professional calculation and analysis tools designed for clarity, confidence, and mathematical rigor.