1001Ferramentas
🌡️ Calculators

Rail Thermal Force (CWR)

Calculate the axial thermal force in a continuous welded rail (CWR), F = E·A·α·ΔT, from the steel elastic modulus E (Pa), the rail section area A (m²), the thermal expansion coefficient α (1/°C) and the temperature change ΔT from the neutral temperature (°C). In CWR — where rails are welded into hundreds-of-metre or kilometre strings, removing joints — thermal expansion is PREVENTED by track fastening, so a temperature change, instead of changing length, generates a huge internal axial force: compression in heat (risk of track buckling, which misaligns the rails) and tension in cold (risk of rail or weld fracture). Since the force does not depend on length (only section and ΔT), it can reach hundreds of kN. So CWR is installed at a neutral (stress-free) temperature chosen mid-range, minimizing compression and tension extremes. This is essential to modern track safety and to set the laying neutral temperature. Enter the elastic modulus, section area, expansion coefficient and temperature change.

Result

Força térmica em trilho contínuo (CWR)

A força axial térmica em um trilho longo soldado (CWR — Continuous Welded Rail) é F = E·A·α·ΔT, a partir do módulo de elasticidade do aço E, da área da seção do trilho A, do coeficiente de dilatação térmica α e da variação de temperatura ΔT em relação à temperatura neutra. O trilho longo soldado — em que os trilhos são soldados em barras de centenas de metros ou quilômetros, eliminando as juntas (e aquele clássico 'tac-tac' dos trens antigos) — trouxe uma via muito mais lisa, silenciosa e durável, mas com um desafio crítico: a dilatação térmica é impedida pela fixação na via. Como o trilho não pode mudar de comprimento, a variação de temperatura gera uma enorme força axial interna: compressão no calor (e o risco do temido buckling — a flambagem lateral da via, que a deforma em curvas serpenteantes e pode descarrilar trens) e tração no frio (risco de ruptura frágil do trilho ou das soldas). O detalhe assustador é que a força não depende do comprimento do trilho — apenas da seção e do ΔT —, podendo atingir centenas de kN mesmo em um trilho de seção modesta. A engenharia lida com isso instalando o CWR a uma temperatura neutra (de fixação ou de assentamento) cuidadosamente escolhida no meio da faixa térmica esperada na região, de modo que os extremos de compressão (no verão) e de tração (no inverno) fiquem equilibrados e dentro dos limites seguros. Calcular essa força é essencial para a segurança da via permanente moderna, para definir a temperatura neutra e para projetar os aparelhos de dilatação nas extremidades e pontos críticos. Informe o módulo de elasticidade, a área da seção, o coeficiente de dilatação e a variação de temperatura.

Related Tools

🛤️

Railway Cant (Superelevation)

Calculate the theoretical equilibrium cant (superelevation) of a railway curve, h = (B·V²) ÷ (127·R), from the dynamic gauge B (mm, distance between rail centers, ~1500 mm on standard gauge), the speed V (km/h) and the curve radius R (m). Cant is the raising of the outer rail above the inner one in curves, tilting the track inward — so the train's weight component helps provide centripetal force, balancing the centrifugal acceleration felt by passengers and reducing wheel-rail lateral wear. Equilibrium cant fully cancels the unbalanced lateral acceleration for a given speed; in practice a lower cant is adopted, since trains run at varied speeds on the same curve, and construction limits (~150-160 mm) apply for comfort and overturning safety of stopped trains. The difference between equilibrium and applied cant is the cant deficiency (or excess). Enter the gauge, speed and curve radius.

🪵

Track Sleeper Count

Calculate the number of sleepers needed in a track section, N = length ÷ spacing, from the section length (m) and the sleeper spacing (m, center to center). Sleepers (cross-ties) are the transverse track elements that carry the rails, hold the gauge (correct rail spacing), transmit rail loads to the ballast over a larger area, and anchor the track against longitudinal and lateral movement. Sleeper spacing (the 'sleeper density', typically 0.55-0.68 m, or about 1500-1900 sleepers per kilometre) is a design parameter depending on axle load, speed and sleeper type (wood, concrete, steel): heavy-haul lines use closer sleepers (more per km) to better spread high loads. This is essential for quantity take-off and budgeting of railway construction or renewal, since sleepers are a main track input, and for laying logistics planning. Enter the section length and the sleeper spacing.

🚃

Railcar Axle Load

Calculate a rail vehicle's axle load, P_axle = total weight ÷ number of axles, from the gross weight of the wagon or locomotive (N, tare plus load) and the number of axles. Axle load is the most important parameter for track design: it is the force each axle transmits to the track (and, per wheel, to each rail), governing stresses in the rail, sleepers, ballast and subgrade. Railways are classified by their axle-load capacity: heavy-haul railways (such as ore lines) run at 30-40 tonnes per axle and need heavy rail, concrete sleepers and reinforced ballast; passenger and light-freight lines run lower loads. Exceeding the allowable axle load causes accelerated fatigue, permanent deformation and failures — so rolling-stock and track-class compatibility is strictly controlled. Axle load also limits maximum train weight and thus transport productivity. Enter the total weight and the number of axles.

The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.