{ "openapi": "3.1.1", "info": { "title": "Shelf Sag & Deflection Calculator API", "version": "1.0.0", "summary": "Check how much a shelf sags under books or a point load, with creep and a front edge strip.", "description": "Every endpoint performs the same calculation as the human page and returns inputs, result, units, assumptions, sources, warnings and computedAt. MCP endpoint: /mcp." }, "servers": [ { "url": "https://kerfwiseshelfsag.usefulweb.app" } ], "paths": { "/api/v1/calculate": { "post": { "operationId": "calculate", "summary": "Check how much a shelf sags under books or a point load, with creep and a front edge strip.", "description": "Calculate the mid-span sag of a shelf from its span, depth, thickness and material under a uniform and a point load, simply supported or fixed. Includes self-weight, long-term creep and a glued front strip or face-frame rail, and suggests a thickness, strip height or support.\n\nMethodology:\n- Euler–Bernoulli beam, maximum at mid-span: simply supported δ = 5wL⁴/(384EI) + PL³/(48EI); both ends fixed δ = wL⁴/(384EI) + PL³/(192EI). w = uniform load plus self-weight (density × g × section area), P = point load × g (g = 9.80665 m/s²).\n- Composite section by the transformed-section method: a front strip with its top flush with the shelf is scaled by n = E_strip / E_shelf; the neutral axis and I follow from the parallel-axis theorem.\n- Long-term (creep) deflection follows EN 1995-1-1 §2.3.2.2 for a permanent load: every part uses E / (1 + k_def) with k_def for service class 1 (solid wood 0.6, plywood 0.8, OSB/3 and P6 1.5, P4 particleboard and MDF 2.25).\n- Moduli are typical: solid wood from the USDA Wood Handbook (clear wood, 12 % moisture content), panels from EN 12369-1 mean values, P2 furniture board from the EN 312 minimum requirement and birch plywood from the Handbook of Finnish Plywood. Use the custom modulus for your board.\n- Suggestions: the thickness or strip height that just meets the limit (bisection, rounded up to 1 mm), the longest span that passes and the sag with a centre support (two separate half spans, conservative).\n\nA serviceability estimate, not a strength check: bending stress, pin and joint strength, knots, moisture and shelf-pin rocking are not included. Real boards vary; a test load tells the truth.", "tags": [ "apps" ], "x-mcp-tool": "kerfwise_shelf_sag", "x-owner-app": "kerfwise", "requestBody": { "required": true, "content": { "application/json": { "schema": { "$ref": "#/components/schemas/KerfwiseShelfSagInput" }, "examples": { "example1": { "summary": "MDF bookshelf, 762 mm span, a full row of books", "value": { "span": 762, "depth": 277, "thickness": 18, "material": "mdf", "uniformLoad": 33, "limit": "L/300" } }, "example2": { "summary": "Same shelf with a 38 mm oak front strip", "value": { "span": 762, "depth": 277, "thickness": 18, "material": "mdf", "uniformLoad": 33, "limit": "L/300", "stripHeight": 38, "stripThickness": 19, "stripMaterial": "oak-red" } }, "example3": { "summary": "Birch plywood shelf, 900 mm, 20 kg point load, short-term", "value": { "span": 900, "depth": 300, "thickness": 18, "material": "ply-birch", "uniformLoad": 0, "pointLoad": 20, "longTerm": false, "limit": "L/360" } }, "example4": { "summary": "Solid red oak, glued housings, 0.02 in per foot rule", "value": { "span": 1000, "depth": 250, "thickness": 22, "material": "oak-red", "support": "fixed", "uniformLoad": 30, "limit": "L/600" } } } } } }, "responses": { "200": { "description": "Calculation result envelope.", "content": { "application/json": { "schema": { "$ref": "#/components/schemas/KerfwiseShelfSagResult" } } } }, "400": { "description": "Malformed JSON body.", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "422": { "description": "Invalid input (see errors[]).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } }, "429": { "description": "Rate limit exceeded (see Retry-After).", "content": { "application/problem+json": { "schema": { "$ref": "#/components/schemas/Problem" } } } } } } }, "/api/v1/tool": { "get": { "operationId": "getToolDefinition", "summary": "Inputs, output schema and examples for this tool", "responses": { "200": { "description": "Tool definition.", "content": { "application/json": { "schema": { "type": "object" } } } } } } } }, "components": { "schemas": { "Problem": { "type": "object", "description": "RFC 9457 problem details. 422 responses include per-field `errors`.", "required": [ "type", "title", "status", "detail" ], "properties": { "type": { "type": "string" }, "title": { "type": "string" }, "status": { "type": "integer" }, "detail": { "type": "string" }, "code": { "type": "string" }, "errors": { "type": "array", "items": { "type": "object", "required": [ "field", "message" ], "properties": { "field": { "type": "string" }, "message": { "type": "string" } } } } } }, "KerfwiseShelfSagInput": { "type": "object", "additionalProperties": false, "properties": { "span": { "title": "Span between supports", "type": "number", "minimum": 50, "maximum": 5000, "default": 762, "x-unit": "mm" }, "depth": { "title": "Shelf depth (front to back)", "type": "number", "minimum": 20, "maximum": 2000, "default": 277, "x-unit": "mm" }, "thickness": { "title": "Shelf thickness", "type": "number", "minimum": 3, "maximum": 100, "default": 18, "x-unit": "mm" }, "material": { "title": "Shelf material", "type": "string", "enum": [ "pb-p2", "pb-p4", "pb-p6", "mdf", "osb3", "ply-birch", "ply-birch-cross", "oak-red", "oak-white", "maple-sugar", "maple-red", "beech", "birch-yellow", "cherry", "walnut", "ash-white", "poplar", "douglas-fir", "pine-white" ], "default": "mdf" }, "customE": { "title": "Custom modulus of elasticity (optional)", "description": "Replaces the material value, for example from the board maker’s data sheet.", "type": "number", "minimum": 100, "maximum": 30000, "x-unit": "N/mm²" }, "support": { "title": "Supports", "type": "string", "enum": [ "simple", "fixed" ], "default": "simple" }, "uniformLoad": { "title": "Uniform load along the shelf", "description": "A full row of books is about 30–40 kg per metre on a 300 mm deep shelf.", "type": "number", "minimum": 0, "maximum": 2000, "default": 33, "x-unit": "kg/m" }, "pointLoad": { "title": "Point load at mid-span", "type": "number", "minimum": 0, "maximum": 2000, "default": 0, "x-unit": "kg" }, "selfWeight": { "title": "Include the shelf’s own weight", "type": "boolean", "default": true }, "longTerm": { "title": "Long-term load (include creep)", "type": "boolean", "default": true }, "limit": { "title": "Sag limit", "type": "string", "enum": [ "L/240", "L/300", "L/360", "L/600" ], "default": "L/300" }, "stripHeight": { "title": "Front strip height (optional)", "description": "A solid edge strip or face-frame rail glued to the front edge, top flush with the shelf. Empty = none.", "type": "number", "minimum": 3, "maximum": 300, "x-unit": "mm" }, "stripThickness": { "title": "Front strip thickness", "type": "number", "minimum": 3, "maximum": 100, "default": 19, "x-unit": "mm" }, "stripMaterial": { "title": "Front strip material", "type": "string", "enum": [ "pb-p2", "pb-p4", "pb-p6", "mdf", "osb3", "ply-birch", "ply-birch-cross", "oak-red", "oak-white", "maple-sugar", "maple-red", "beech", "birch-yellow", "cherry", "walnut", "ash-white", "poplar", "douglas-fir", "pine-white" ], "default": "oak-red" } }, "required": [] }, "KerfwiseShelfSagResult": { "type": "object", "additionalProperties": false, "required": [ "schemaVersion", "tool", "computedAt", "inputs", "summary", "result", "units", "assumptions", "sources", "warnings", "presentation", "links" ], "properties": { "schemaVersion": { "type": "string", "const": "1.0" }, "tool": { "type": "object", "additionalProperties": false, "required": [ "id", "name", "version" ], "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "version": { "type": "string" } } }, "computedAt": { "type": "string", "format": "date-time" }, "inputs": { "type": "object", "description": "Normalised inputs actually used, including applied defaults." }, "summary": { "type": "string" }, "result": { "type": "object", "additionalProperties": false, "required": [ "verdict", "passes", "material", "stiffener", "section", "sectionLongTerm", "loads", "deflection", "limit", "limitMm", "ratio", "spanOver", "suggestions", "warnings" ], "properties": { "verdict": { "type": "string" }, "passes": { "type": "boolean" }, "material": { "type": "object", "properties": { "id": { "type": "string" }, "name": { "type": "string" }, "eMpa": { "type": "number" }, "densityKgM3": { "type": "number" }, "kdef": { "type": "number" }, "source": { "type": "string" } } }, "stiffener": { "type": [ "object", "null" ], "properties": { "material": { "type": "string" }, "name": { "type": "string" }, "eMpa": { "type": "number" }, "kdef": { "type": "number" } } }, "section": { "type": "object", "description": "Transformed section (instantaneous moduli): neutral axis from the top, I in mm⁴, EI in N·mm²." }, "sectionLongTerm": { "type": "object", "description": "Transformed section with E / (1 + k_def) per part." }, "loads": { "type": "object", "properties": { "selfNPerMm": { "type": "number" }, "uniformNPerMm": { "type": "number" }, "pointN": { "type": "number" }, "totalKg": { "type": "number" } } }, "deflection": { "type": "object", "properties": { "selfMm": { "type": "number" }, "uniformMm": { "type": "number" }, "pointMm": { "type": "number" }, "instantMm": { "type": "number" }, "longTermMm": { "type": "number" }, "creepFactor": { "type": "number" }, "checkedMm": { "type": "number" } } }, "limit": { "enum": [ "L/240", "L/300", "L/360", "L/600" ] }, "limitMm": { "type": "number" }, "ratio": { "type": "number" }, "spanOver": { "type": [ "number", "null" ] }, "suggestions": { "type": "object", "properties": { "thicknessMm": { "type": [ "number", "null" ] }, "stiffenerHeightMm": { "type": [ "number", "null" ] }, "maxSpanMm": { "type": "number" }, "midSupportMm": { "type": "number" } } }, "warnings": { "type": "array", "items": { "type": "string" } } } }, "units": { "type": "object", "additionalProperties": { "type": "string" } }, "assumptions": { "type": "array", "items": { "type": "string" } }, "sources": { "type": "array", "items": { "type": "object", "additionalProperties": false, "required": [ "title" ], "properties": { "title": { "type": "string" }, "url": { "type": "string" }, "publisher": { "type": "string" }, "retrievedAt": { "type": "string" }, "note": { "type": "string" } } } }, "warnings": { "type": "array", "items": { "type": "string" } }, "presentation": { "type": "array", "items": { "type": "object" }, "description": "Display blocks used by the human page (same data)." }, "links": { "type": "object", "additionalProperties": false, "required": [ "human", "api", "openapi", "methodology" ], "properties": { "human": { "type": "string", "format": "uri" }, "api": { "type": "string", "format": "uri" }, "openapi": { "type": "string", "format": "uri" }, "methodology": { "type": "string", "format": "uri" } } } } } } } }