How is the stress area of a bolt calculated?

The tensile stress area As is calculated as As = (π/4) × ((d₂ + d₃)/2)², where d₂ is the pitch diameter and d₃ is the minor diameter of the external thread. This formula accounts for the thread root geometry and gives the effective cross-section for tensile loading per ISO 898-1.

What is the difference between pitch diameter and minor diameter?

The pitch diameter (d₂) is the diameter where the thread tooth width equals the space width — it's the key dimension for thread fit. The minor diameter (d₃) is the smallest diameter at the root of the external thread. The minor diameter determines the core cross-section of the bolt.

What is the difference between coarse and fine pitch thread dimensions?

For the same nominal diameter, fine pitch threads have a smaller pitch (P), resulting in a larger pitch diameter and minor diameter compared to coarse threads. This gives fine pitch bolts a larger stress area — for example, M12×1.25 fine has As ≈ 92 mm² versus M12 coarse (P=1.75) with As ≈ 84.3 mm². Fine pitch threads provide better resistance to loosening from vibration.

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公制螺紋尺寸計算器

查詢公制 ISO 螺紋的所有關鍵尺寸——中徑、小徑、應力面積、核心面積——涵蓋 M3 至 M48 的粗牙與細牙螺距。

ISO 261 ISO 724 M3 – M48

結果

螺紋標稱

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公稱直徑 d

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螺距 P

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中徑 d₂

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小徑 d₃（螺栓）

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小徑 D₁（螺母）

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螺紋高度 H

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應力面積 Aₛ

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核心面積 A₃

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螺紋	d (mm)	P (mm)	d₂ (mm)	d₃ (mm)	D₁ (mm)	H (mm)	Aₛ (mm²)	A₃ (mm²)

ISO 公制螺紋幾何形狀

根據 ISO 261 與 ISO 724，ISO 公制螺紋的基本輪廓由基本三角形高度 H₁ 與螺距 P 定義。

中徑與小徑

外螺紋（螺栓）的中徑 d₂ 與小徑 d₃ 由公稱直徑 d 與螺距 P 導出：

內螺紋（螺母）的小徑 D₁：

應力面積與核心面積

抗拉應力面積 A_s （依據 ISO 898-1）與核心面積 A₃ 為：

ℹ️ 注意： 應力面積 A_s 是計算螺栓抗拉與保證負荷時使用的有效截面積。它大於核心面積 A₃，因為它取中徑與小徑的平均值。

實務範例

範例——M12 粗牙螺距

已知： d = 12 mm, P = 1.75 mm

H = 0.866025 × 1.75 = 1.5155 mm

d₂ = 12 − 0.6495 × 1.75 = 10.863 mm

d₃ = 12 − 1.2269 × 1.75 = 9.853 mm

A_s = (π/4) × ((10.863 + 9.853)/2)² = 84.3 mm²

A₃ = (π/4) × 9.853² = 76.2 mm²