What is the tensile stress area of a bolt?

The tensile stress area (As) is the effective cross-sectional area used to calculate the tensile load capacity of a threaded fastener. It is smaller than the nominal shank area because it accounts for the thread root geometry. It is defined in ISO 898-1 and depends on the pitch diameter and minor diameter of the thread.

How is bolt tensile strength calculated?

Bolt ultimate tensile load is calculated as Ft = Rm × As, where Rm is the ultimate tensile strength of the bolt material (determined by property class) and As is the tensile stress area. For example, a class 8.8 bolt has Rm = 800 MPa.

What does bolt property class 8.8 mean?

The first number (8) represents 1/100th of the minimum ultimate tensile strength in MPa (800 MPa). The second number (8) represents 10× the ratio of yield strength to ultimate tensile strength (0.8). So yield = 800 × 0.8 = 640 MPa.

How is bolt shear strength calculated?

ISO 898-1 does not specify shear strength — it covers tensile and proof-load properties only. A common simplified estimate takes shear strength as 60% of tensile strength: Fs = 0.6 × Rm × As, based on the von Mises yield criterion. Design codes such as Eurocode 3 (EN 1993-1-8) apply their own factors (0.6 or 0.5 depending on property class) plus partial safety factors. For single shear, use one stress area; for double shear, multiply by 2.

What is the difference between proof load and tensile strength?

Proof load is the maximum force a bolt can withstand without permanent deformation (elastic limit). Ultimate tensile strength is the maximum force before fracture. The proof load stress (Sp) is approximately 90% of the yield strength for most property classes.

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螺栓抗拉與抗剪強度計算器

依據 ISO 898-1 性能等級資料計算公制螺栓之極限拉伸負荷，並提供簡化之剪力承載力估算。請選擇螺栓尺寸與性能等級。

ISO 898-1 M3 – M64 等級 4.6 – 12.9

螺栓尺寸

性能等級

剪切面

快速預設

結果

極限抗拉負荷 (Ft)

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剪力承載力（Fs，簡化估算）

—

抗拉應力面積 (As)

—

屈服負荷 (Fy)

—

極限抗拉強度 (Rm)

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極限抗拉負荷

螺栓在斷裂前可承受的最大拉力：

R_m — 極限抗拉強度 (MPa)，來自性能等級
A_s — 抗拉應力面積 (mm²)，來自 ISO 898-1 / ISO 261

剪力承載力（簡化估算）

ISO 898-1 規範了螺栓之拉伸與保證負荷特性，並未不規定剪力強度。此處顯示之數值為廣泛採用之簡化工程估算，將剪力強度視為拉伸強度之約 60%（基於 von Mises 準則，τ ≈ 0.58 σ）：

對於雙剪切，乘以 2（兩個剪切面）。

⚠️ 剪力設計注意事項： 實際剪力承載力取決於剪力面是否穿過螺紋或無螺紋桿部、接頭滑移與板件承壓，以及疲勞載荷。設計規範各自定義其數值——例如 Eurocode 3（EN 1993-1-8）採用 F_v = α_v × f_ub × A，其中 α_v = 0.6 適用於 4.6、5.6 與 8.8 級，但 4.8、5.8、6.8 與 10.9 級則為 0.5，並配合部分安全係數。剪力承載接頭設計務必依據適用之結構或機械設計規範進行驗證，不可僅依賴此簡化估算。

依 ISO 898-1 的性能等級

級別	Rm (MPa)	Rp0.2 (MPa)	典型用途
4.6	400	240	低強度，一般用途
5.8	520	420	結構用，非預壓
8.8	800	640	汽車、機械（最常見）
10.9	1040	940	高強度結構用
12.9	1220	1100	最高強度（合金鋼）

實務範例

範例 — M10 × 8.8 螺栓

已知： M10 螺栓，性能等級 8.8，單剪切

A_s = 58.0 mm², R_m = 800 MPa

F_t = 800 × 58.0 = 46,400 N = 46.4 kN

F_s = 0.6 × 800 × 58.0 = 27,840 N = 27.8 kN

⚠️ 注意： 這些為未考慮安全係數之極限承載力。設計時應套用適當之安全係數（靜態載荷通常為 2–3，疲勞載荷為 4–6）。