Mgawo wa upanuzi wa joto (CTE) ni nini?

CTE (α) is the fractional change in length per degree of temperature change. Units: µm/(m·°C) or 10⁻⁶/°C. Example: steel α ≈ 12 µm/(m·°C) means a 1m bar grows 12 µm per 1°C rise.

Ninavyokokotoa msongo wa joto katika kipande kilichozuiwa?

When expansion is fully restrained: σ = E × α × ΔT. For steel at ΔT = 100°C: σ = 200,000 × 12e-6 × 100 = 240 MPa — nearly yield stress!

Upanuzi wa ujazo ni nini?

For isotropic materials, volumetric CTE ≈ 3 × linear CTE. Volume change: ΔV = V₀ × 3α × ΔT. Important for tanks, pipes, and enclosed fluid systems.

Ninawezaje kupima ukubwa wa kitanzi cha upanuzi cha mabomba?

Guided-cantilever formula: loop leg length L = √(3 × E × D × Δ / Sₐ), where E = elastic modulus (MPa), D = pipe OD (mm), Δ = expansion (mm), Sₐ = allowable stress range (MPa); L in mm. Rule of thumb for carbon steel (E ≈ 200 GPa, Sₐ ≈ 138 MPa): L ≈ 66 × √(D × Δ) in mm.

Je, CTE hubadilika kulingana na joto?

Ndiyo. CTE kwa kawaida huongezeka kidogo kadri joto linavyoongezeka. Thamani zilizotolewa ni wastani wa masafa fulani (kwa kawaida 20–100°C). Kwa kazi za joto la chini sana au joto la juu sana, tumia data maalum kwa masafa halisi ya joto.

Zana ya Uhandisi Isiyolipisha

Kikokotoo cha Upanuzi wa Joto

Calculate linear and volumetric thermal expansion for 20+ materials. Pipe expansion between anchors, expansion loop sizing, and thermal stress when constrained (σ = E·α·ΔT).

Mstari & Ujazo20+ MaterialsThermal StressPipe Expansion

Material

CTE α (×10⁻⁶ /°C)

Urefu wa Awali (mm)

Mabadiliko ya Joto ΔT (°C)

Kiasi cha Awali (cm³ — hiari, kwa upimaji wa ujazo)

Moduli wa Elastiki E (GPa — kwa hesabu ya msongo)

Quick presets

Matokeo ya Upanuzi

Upanuzi wa Mstari ΔL

—

Upanuzi katika mm

—

Upanuzi katika µm

—

Upanuzi katika mils

—

New Length

—

Strain ε

—

Msongo wa Joto (ikiwa umezuiwa)

—

Nguvu ya Joto (kwa kila cm² ya eneo)

—

Upanuzi wa Ujazo ΔV

—

Kitanzi cha Upanuzi (bomba la chuma, kanuni ya haraka)

—

Upanuzi wa Mstari

Where α is the coefficient of thermal expansion (CTE) in 1/°C, L₀ is the original length, and ΔT is the temperature change.

Upanuzi wa Ujazo

Kwa vifaa vya isotropiki, CTE ya ujazo ni takriban mara 3 ya CTE ya mstari.

Msongo wa Joto (Kipande Kilichozuiwa)

Wakati upanuzi unazuiwa kabisa (mfano, bomba kati ya nanga mbili imara), msongo unaotokana unaweza kuwa mkubwa sana. Msongo huu ni wa mkandamizo wakati wa joto na wa mvutano wakati wa baridi.

Upimaji wa Kitanzi cha Upanuzi (Kanuni ya Haraka)

Where D is the pipe outer diameter (mm) and Δ is the expansion (mm); the result L is in mm. The factor 66 comes from the guided-cantilever formula L = √(3 · E · D · Δ / Sₐ) evaluated for carbon steel (E = 200 GPa, Sₐ = 138 MPa). For other materials or allowable stresses use the full formula (L scales as √(E/Sₐ)). This is a screening estimate, not a full code flexibility analysis.

Mfano wa Vitendo

Mfano — Bomba la Chuma cha Kaboni la 6m, ΔT = 80°C

Given: L₀ = 6000 mm, α = 12 × 10⁻⁶ /°C, ΔT = 80°C, E = 200 GPa

ΔL = 12e-6 × 6000 × 80 = 5.76 mm

Thermal stress if constrained: σ = 200,000 × 12e-6 × 80 = 192 MPa

Expansion loop (DN100/OD 114 mm): L ≈ 66 × √(114 × 5.76) ≈ 1,690 mm ≈ 1.7 m

Hifadhidata ya CTE ya Vifaa

Material	α (×10⁻⁶ /°C)	E (GPa)	Notes
Carbon steel	12.0	200	SA-516, P265GH
Chuma cha aloi ya chini	12.5	200	16Mo3, SA-387
Chuma cha Cr-Mo (2.25Cr)	12.0	205	SA-335 P22
Stainless 304	17.3	193	1.4301, 18Cr-8Ni
Stainless 316	16.0	193	1.4401, 16Cr-10Ni-2Mo
Stainless 321	17.0	193	1.4541, iliyoimarishwa na Ti
Duplex 2205	13.0	200	1.4462
Aluminium 6061	23.6	69	T6 temper
Copper	17.0	117	Pure, annealed
Brass (CuZn30)	20.0	110	Shaba ya cartridge
Bronze (CuSn8)	18.0	110	Bronzi ya fosforasi
Titanium Gr.2	8.6	103	Safi kibiashara
Nickel 200	13.3	207	Pure nickel
Inconel 625	12.8	207	Ni-Cr-Mo
Inconel 718	13.0	211	Ni-Cr-Fe
Grey cast iron	10.5	110	GG25
Chuma geupe cha nguvu (Ductile cast iron)	11.0	170	GGG40
Concrete	12.0	30	Hutofautiana kulingana na mchanganyiko
Kioo (soda-lime)	9.0	72	Window glass
PTFE (Teflon)	120.0	0.5	Very high CTE
HDPE	150.0	1.0	Polyethylene
PVC	80.0	3.0	Rigid PVC
Invar 36	1.2	145	Aloi yenye CTE ya chini sana

💡 Note: Thamani za CTE ni wastani kwa joto la 20–100°C. Kwa matumizi ya joto la juu au baridi kali, tumia data maalum kutoka kwa viwango vya nyenzo.