267 QStrength of Bolt 1)Tensile Load Bolt P= t×As ·······(1) =πd2 t/4 ·····(2) (Ex.)The proper size of a hexagon socket head cap screws, which is to bear a repeated tensile load (pulsating) at P=1960N {200 kgf} , should be determined. (The hexagon socket head cap screws are SCM435, 38 to 43 HRC, strength class 12.9) (1) Using Equation As=Pt/ t =1960/219.6 =8.9 [mm2] By finding a value greater than the result of the equation in the Effective Sectional Area column in the table on the right, M5, 14.2 [mm2], should be selected. M6, allowable load of 2087N {213 kgf} , should be selected from the column for strength class 12.9, if the fatigue strength is considered. 2) If the bolt, like a stripper bolt, is to bear a tensile impact load, the right size should be selected from the fatigue strength column. (Under a load of 1960N {200kgf}, stripper bolt made of SCM435, 33 to 38 HRC, strength class 10.9) By finding a value greater than the allowable load of 1960N {200 kgf} in the Strength Class 10.9 column in the table on right, M8, 3116[N] {318[kgf]} , should be selected. Hence, MSB10 with the M8 threaded portion and an axial diameter of 10 mm should be selected. If it is to bear a shearing load, a dowel pin should also be used. QStrength of Screw Plug When screw plug MSW30 is to bear an impact load, allowable load P should be determined. (The materials of MSW30 are S45C, 34 to 43 HRC, tensile strength t 637N/mm2 {65kgf/mm2.} ) If M S W is shorn at a spot within the root diameter section and is broken, allowable load P can be calculated as shown below. Allowable Load P = t×A =3.9×107.4 =40812[N] {4164[kgf]} Find the allowable shearing force base on the core diameter of female thread if a tap is made of soft material. QStrength of Dowel Pins The proper size of a dowel pin under repeated shearing load of 7840N {800 kgf} (Pulsating) should be determined as follows. (The material of Dowel Pins is SUJ2. Hardness 58HRC~) P=A× =πD2 /4 D= (4P) / (π ) = (4×7840) / (3.14×188) ≈7.3 D8 or a larger size should be selected for MS. If the dowel pins are of a roughly uniform size, the number of the necessary tools and extra pins can be reduced. The yield stress, strength class 12.9, is b=1098[N/mm2] {112[kgf/mm2]}. Allowable Stress t= b/Safety Factor(from the above table Safety Factor 5) =1098/5 =219.6[N/mm2] {22.4[kgf/mm2]} Pt : Tensile Load in the Axial Direction [N] b : Yield Stress of the Bolt [N/mm2] t : Allowable Stress of the Bolt [N/mm2] ( t= b/Safety Factor ) As : Effective Sectional Area of the Bolt [mm2] As=πd2/4 d : Effective Dia. of the Bolt (Core Dia.) [mm] Typical strength calculations are presented here. In practice, further conditions including hole-to-hole pitch precision, hole perpendicularity, surface roughness, circularity, plate material, parallelism, quenching or non-quenching, precision of the press, product output, wear of tools should be considered. Hence the values in these examples are typical but not guaranteed values. Area A=Root Diameter d1×π×L (Root Diameter d1≈M−P) A=(M−P)πL=(30−1.5)π×12 =1074 [mm2] Yield Stress≈0.9×Tensile Strength b=0.9×637=573[N/mm2] Shearing Stress≈0.8×Yield Stress =459 [N/mm2] Allowable Shearing Stress t=Shearing Stress/Safety Factor 12 =459/12=38 [N/mm2] {3.9 [kgf/mm2]} Yield Stress for SUJ2 b=1176 [N/mm2] {120 [kgf/mm2]} Allowable Shearing Strength = b×0.8/Safety Factor =1176×0.8/5 =188 [N/mm2] {19.2 [kgf/mm2]} Allowable Stress = Reference Strength Safety Factor Reference Strength: Yield Stress for Ductile Material Fracture Stress for Fragile Material QSafety Factor of Unwin Based on Tensile Strength M P P Root Diameter d1 The dowel pin must not be loaded. QFatigue Strength of Bolt (Thread:Fatigue Strength is 2 million times) Nominal of Thread Effective Sectional Area As mm2 Strength Class 12.9 10.9 Fatigue Strength† Allowable Load Fatigue Strength† Allowable Load N/mm2 [kgf /mm2] N {kgf} N/mm2 [kgf /mm2] N {kgf} M 4 8.78 128{ 13.1} 1117{ 114} 89{ 9.1} 774{ 79} M 5 14.2 111{ 11.3} 1568{ 160} 76{ 7.8} 1088{ 111} M 6 20.1 104{ 10.6} 2087{ 213} 73{ 7.4} 1460{ 149} M 8 36.6 87{ 8.9} 3195{ 326} 85{ 8.7} 3116{ 318} M10 58 73{ 7.4} 4204{ 429} 72{ 7.3} 4145{ 423} M12 84.3 66{ 6.7} 5537{ 565} 64{ 6.5} 5370{ 548} M14 115 60{ 6.1} 6880{ 702} 59{ 6} 6762{ 690} M16 157 57{ 5.8} 8928{ 911} 56{ 5.7} 8771{ 895} M20 245 51{ 5.2} 12485{ 1274} 50{ 5.1} 12250{ 1250} M24 353 46{ 4.7} 16258{ 1659} 46{ 4.7} 16258{ 1659} Fatigue strength* is a revision of an excerpt from "Estimated Fatigue Limits of Small Screws, Bolts and Metric Screws for Nuts" (Yamamoto). Materials Static Load Repeated Load Impact Load Pulsating Reversed Steel 3 5 8 12 Cast Iron 4 6 10 15 Copper, Soft Metal 5 5 9 15 GeneralTechnical Information Strength of Bolts, Screw Plugs and Dowel Pins
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