Bolted cylinder-head joint — preload and bolt grade: 25-Nav-B1 Applied Thermodynamics and Heat Transfer (25-Mec-A1), May 2013, Q5

Question 5: Bolted cylinder-head joint — preload and bolt grade (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. 8 × M12 steel bolts; sealing diameter $D_s=150\text{ mm}$; gas pressure $p=6\text{ MPa}$; grip $l = D+E = 20+25 = 45\text{ mm}$ (steel head on steel flange); confined gasket (gasket carries no share of stiffness). $A_t=84.3\text{ mm}^2$ (M12 coarse); $E_{steel}=207\text{ GPa}$; $n_{sep}\ge1.5$, $n_{yield}\ge2$.

Find. the required bolt preload $F_i$ and a suitable metric bolt grade.

Steel head ($D=20$) bolted to the steel flange ($E=25$); grip $l=45\text{ mm}$. Internal gas pressure over the $150\text{ mm}$ seal tends to separate the joint.

Approach. Compute the total separating force from pressure over the sealing area and share it among 8 bolts. Find the joint stiffness constant $C=k_b/(k_b+k_m)$ from the bolt and member stiffnesses; the external load raises bolt tension by only $C\,P$. Size the preload for the separation factor, then choose a grade so the proof strength meets the yielding factor.

External load per bolt. Total end thrust $P_{tot}=p\,\tfrac{\pi}{4}D_s^2 = 6\times10^6\,\tfrac{\pi}{4}(0.150)^2 = 106\text{ kN}$; per bolt $$P = \frac{106\,000}{8} = 13.25\text{ kN}.$$
Bolt and member stiffness. With grip $l=45\text{ mm}$, $A_t=84.3\text{ mm}^2$, $A_d=113\text{ mm}^2$ (shank), the bolt stiffness is $k_b\approx 424\text{ MN/m}$; the members (steel, frustum method) give $k_m\approx 2312\text{ MN/m}$. Hence the joint constant $$C = \frac{k_b}{k_b+k_m} = \frac{424}{424+2312} = 0.155.$$
Preload for separation ($n_0\ge1.5$). The joint opens when the external load reaches $F_i/(1-C)$, so $$F_i = n_0\,P\,(1-C) = 1.5(13\,250)(1-0.155).$$ $$\boxed{F_i \approx 16.8\text{ kN}.}$$
Bolt grade for yielding ($n_p\ge2$). The proof strength must satisfy $S_p A_t \ge F_i + n_p C P$: $$S_p \ge \frac{16\,800 + 2(0.155)(13\,250)}{84.3\times10^{-6}} = 248\text{ MPa}.$$ Metric grade 5.8 ($S_p=380\text{ MPa}$) clears this comfortably; its yielding factor is $$n_p = \frac{S_pA_t - F_i}{CP} = \frac{380(84.3) - 16\,800}{0.155(13\,250)} = 7.4 \ge 2,$$ and $F_i = 16.8\text{ kN} \le 0.75\,S_pA_t = 24.0\text{ kN}$, a sound preload level. $$\boxed{\text{Select grade 5.8 metric bolts, } F_i \approx 16.8\text{ kN.}}$$ (The minimum grade that meets $S_p\ge248\text{ MPa}$ is 4.8; 5.8 is recommended for availability and margin.)

Question 5 — results
Quantity	Value
Total end thrust $P_{tot}$	$106\text{ kN}$
External load / bolt $P$	$13.25\text{ kN}$
Joint constant $C$	$0.155$
Required preload $F_i$	$16.8\text{ kN}$
Bolt grade	Metric 5.8 ($S_p=380\text{ MPa}$), $n_p=7.4$

Check / assumptions: A confined gasket carries no joint compliance, so member stiffness is taken as steel-on-steel over the $45\text{ mm}$ grip (frustum method). Standard M12 coarse-thread $A_t=84.3\text{ mm}^2$ is used; bolt length is taken as the grip for stiffness. Proof strengths follow ISO 898-1 (4.8: 310, 5.8: 380 MPa).

Topic: Preloaded bolted joint under a static separating load.

Key relations: $C=k_b/(k_b+k_m)$; bolt load $F_b=F_i+CP$; separation factor $n_0=F_i/[P(1-C)]$; yielding factor $n_p=(S_pA_t-F_i)/(CP)$.

Why this works: Because the stiff steel members carry most of the load path ($C\approx0.15$), only about 15% of each increment of external load reaches the bolt — the rest simply relieves member compression. A preload above $P(1-C)$ keeps the joint clamped (no leakage), while the small $CP$ term keeps the peak bolt stress well below proof.

Common pitfall: Adding the full external load $P$ to the preload instead of only $CP$ (grossly oversizing the bolt), or omitting the $(1-C)$ factor in the separation condition.

Source: Shigley, Mechanical Engineering Design, §8.4–8.7 (stiffness, preload, joint safety factors); Norton §15.

Question 5 of 6: Bolted cylinder-head joint — preload and bolt grade

Question 5: Bolted cylinder-head joint — preload and bolt grade (20 marks)