ENGINEERING ECOSYSTEM

Verified Engineering Solvers & Platforms

Every application in the AskOnlineTutor ecosystem is built on deterministic mathematical foundations, rigorous benchmark validation, and step-by-step educational transparency.

414/414 Beam Solver Tests88/88 Thermo Benchmarks10⁻⁹ Green’s Theorem Precision

LIVE IN WEB APPENGINEERING MODULE 01

Beam Master

Continuous Beam Analysis & 11-Step Mathematical Proofs

A comprehensive 1D beam calculation engine passing 414/414 regression tests. Solves statically determinate and indeterminate continuous multi-spans with point loads, uniform distributed loads (UDL), linearly varying loads (UVL), concentrated moments, and angled forces with axial decomposition.

Test Suite414/414 Passing (100%)

EngineMacaulay & Global Stiffness

LoadsPoint, UDL, UVL, Moments, Angled

FeaturesInternal Hinges, PDF Reports

Deterministic Macaulay double-integration deflection engine

Direct global stiffness matrix formulation for continuous spans

Support for internal hinges with bending moment discontinuity checks

Angled & inclined force decomposition with axial reaction vectors

Complete 11-step mathematical LaTeX derivations and governing equations

High-resolution multi-page vector PDF calculation packet reports

Launch in Web App View Full Guide

LIVE APP (FLUTTER)ENGINEERING MODULE 02

Mohr Master

Plane Stress Transformations & Interactive Mohr's Circle

A specialized 2D plane stress transformation calculator for mechanics of materials. Converts normal and shear stress components (σx, σy, τxy) into principal stresses (σ₁, σ₂) and maximum in-plane shear (τ_max) with real-time synchronized stress element rotation.

MethodologyMohr's Circle & Stress Transformation

Outputsσ₁, σ₂, θ_p, τ_max, θ_s

Edge CasesHydrostatic, Pure Shear, Uniaxial

Educational7-Step Formula Breakdown

Instant principal stress calculation (σ₁, σ₂) and principal angle orientations (θ_p)

Maximum in-plane shear stress (τ_max) and corresponding normal stress (σ_avg)

Arbitrary plane stress transformation at any custom angle θ

Real-time animated Mohr’s Circle plot with synchronized rotating stress element

Comprehensive 7-step pedagogical derivation with substitutions and interpretations

Robust edge case handlers for hydrostatic pressure, pure shear, and uniaxial tension

Launch in Web App

IN DEVELOPMENTENGINEERING MODULE 03

Truss Master

2D Planar Truss Analysis & Hybrid Step-by-Step Solver

A structural analysis platform for 2D pin-jointed trusses. Utilizes a hybrid architecture: a 100% accurate global stiffness matrix backend coupled with pedagogical Method of Joints and Method of Sections generators.

EngineMatrix Stiffness + Equilibrium Solver

MethodsMethod of Joints & Method of Sections

StabilityStatic Determinacy Check (m+r=2j)

TemplatesPratt, Warren, Howe, Fink, K-Truss

Global matrix stiffness engine for guaranteed ground-truth axial member forces

Step-by-step Method of Joints equilibrium derivations for joint-by-joint review

Method of Sections cutting-plane equilibrium with moment center selection

Automated static determinacy and mechanism classification (m + r vs 2j)

Automated zero-force member detection rules (unloaded joints & collinear sets)

Color-coded member visualization distinguishing Tension (blue) and Compression (red)

Engineering StatusIn Active Development

ENGINE VERIFIEDENGINEERING MODULE 04

Section Properties (ZED 2)

Exact Green's Theorem Boundary-Contour Geometric Engine

A clean-room rebuild cross-section analysis engine. Computes area, centroid (x̄, ȳ), second moments of area (Ix, Iy, Ixy), principal axes, and section moduli using Green's theorem boundary integrals with Kahan compensated summation.

Precision10⁻⁹ on Primitives, 10⁻⁶ Off-Origin

IntegrationGreen's Theorem Two-Pass Centered

RobustnessCW/CCW Winding-Robust Contours

LibrariesAISC Steel Shapes & Custom Polygons

Exact boundary-contour evaluation via Green's theorem (no mesh discretization error)

Kahan compensated summation algorithm ensuring numerical stability down to 10⁻⁹

Winding-robust contour handling (automatically resolves inner hole orientations)

Second moments of area (Ix, Iy, Ixy) and principal axes rotation angle (θ_p)

Elastic section moduli (Sx, Sy) and plastic section moduli (Zx, Zy)

Full AISC structural shape database (W, S, C, L, HSS, WT) and custom composite polygons

Engineering StatusExact Engine Proven

88/88 BENCHMARKS (100%)ENGINEERING MODULE 05

ThermoCore

Tiered Thermodynamics & Power Cycle Engine

A high-performance thermodynamics platform featuring 88/88 verified benchmark problems. Integrates CoolProp 7.2.0 for high-accuracy fluid states, 1st & 2nd law device balances, thermodynamic power/refrigeration cycles, and an independent ParseValidator pipeline.

Accuracy88/88 Benchmarks (100.0% Pass Rate)

Fluid EngineCoolProp 7.2.0 EOS & Ideal Gases

CyclesRankine, Brayton, Otto, Diesel, Carnot

VerificationDeterministic ParseValidator

Tier 1 (43/43): High-precision state property evaluation across Water, Refrigerants & Gases

Tier 2 (23/23): 1st & 2nd Law energy balances for nozzles, turbines, heat exchangers & transient CVs

Tier 3 (12/12): Complete cycle models for Rankine (reheat/regenerative), Brayton, Otto & Diesel

Tier 4 (10/10): Psychrometrics, gas mixtures, combustion stoichiometry, and parametric sweeps

Structured REST API (/solve, /psychro, /sweep, /sensitivity) powered by FastAPI

Independent deterministic ParseValidator preventing hallucinated engineering values

Engineering StatusBackend Tested & Verified