165   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

AMERICAN Journal of Engineering,  
Mechanics and Architecture 

Volume 2, Issue 3, 2024 ISSN (E): 2993-2637 

 
  

Calculation of Rod Bolt Strength 
 

Nurova O. S. 

Karshi Institute of Engineering and Economics 

 

Abstract: In this article, it is assumed that under the action of an external force, various stresses 

arise in the bolt joint rod. For example, when only a tensile force is applied to the bolt rod, the 

bolt is strongly tensioned, and when no external force is applied to the bolt rod, the bolt is 

stretched, when a tensile force is applied to the bolt rod from the outside, when the force in the 

bolted joint is directed perpendicular to the axis, when the acting force creates a bending moment 

on the bolt shaft, and the stresses were determined when calculating the bolt end connections.  

Keywords: bolt, rod, hook, thread, yoke, external thread, thread, equivalent, metric thread, 

hermetic. 

 

 

Introduction: Under the influence of an external force, various stresses arise in the rod of a 

bolted connection. 

In this case, the magnitude of stresses in the stern depends on the direction of external forces and 

is determined as follows; 

 

 

 

 

 

 

 

 

 

 

Figure 1 

a) Let only a tensile force act on the bolt shaft. To do this, we can take as an example a hook that 

is not too tight and not stressed (Fig.1). 

Under the influence of an external force, various stresses arise in the bolted connection rod, the 

magnitude of which depends on the direction of the external forces and is determined as follows; 

 

 



 

166   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

 

  

 

 

 

 

  

 

 

 

 

Figure 2 

Its threaded part is checked for elongation under the action of an external force R along the d-

diameter: 

b) The bolt is tightened tightly, and no external force acts on the rod (Fig.2). 

б =
𝑃

𝜋𝑑1
2 4⁄

≤ [б]                                     𝑑1 = √
4𝑃

𝜋[б] 
 

This includes the bolts used to slide and secure the closed transmission cover. As a result of 

tightening, tensile and torsional stresses arise in the bolt shaft, while the stresses created by the 

external tensile force  

b =
4𝑃

𝜋𝑑2
 

The torsional tension created by the torque in the rod thread is: 

 =
𝑇𝑝

𝑤
 =

0,5𝑃𝑑2tg( +p𝐼)

0,2𝑑𝑙
3  

Total (equivalent) voltage in the stern 

бэкв = √б2 + 3  2 = б√1 + 3(
  

б
)2 

here,                                                       
 

б
=

0,5𝑃𝑑2tg( +p𝐼)π𝑑1
2

(𝜋𝑑𝑙
3/16)4𝑃

 

For metric threads with relatively large pitches: 𝑑2 ≈ 1.1𝑑3  𝛽 = 2°30𝐼, p𝐼 = 9°45𝐼 

provided that 
 

б
 ≈ 0,5. In that 𝑑2,, р' for accepted values бэкв ≈ 1,3б 

Therefore, the value of the total force R acting on the bolt shaft when tensile and torsional forces 

are applied is recommended to be taken as indicated above, where the tension value is 

determined as follows: 

  

бэкв ≈ 1,3б =
5.2𝑃

𝜋𝑑1
2 ≤ [б] 

Design diameter of threaded bolt 𝑑1 ≥ √5.2𝑃𝑌 мм. (6). 



 

167   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

Here, [б] = боқ/ [S] — permissible tensile stress for a bolt. боқ— yield strength of the bolt 

material; [S] is the safety factor, its value is taken according to depending on the nature of the 

load, diameter and material of the bolt. 

The bolt is pulled out, and a tensile force is applied to the bolt shaft from the outside. Examples 

of this are bearing units in a closed gear, lids of sealed containers under pressure (Fig.3). Air or 

liquid does not come out of the connection groove when the bolt is pulled out by force Рс, but 

due to the external force Р1, the bolt rod is stretched by the amount ∆l_b. 

 

 

 

 

 

 

 

 

 

 

Figure 3 

When calculating the strength of a bolt in connections, torque is taken into account, as a result 

the bolt must be pulled with the following force. 

In this case, the connection parts are compressed, i.e. ∆𝑙𝑏 = ∆𝑙𝑔. (1— Figure). 

The result is the total value of the forces acting on cj. 𝑃∑  =  𝑃 + 𝑃1 (13) will 

The elongation and compression of the connection parts is influenced by the external force 𝑃1, at 

which 𝑃1 power to the rod, bolt, the rest (1 - power connection details (1 − 𝑃1 ) influences. In 

this case, the total force acting on the shutter rod  

Рум = 𝑃 + 𝑃1 will 

The diameter of the bolt can be determined using formula (1.6), the value of the safety factor is 

selected according to table 1.2. 

d) In a bolted connection, the force is directed perpendicular to the axis. In this case, the bolt can 

be installed in two different ways. 

1) There is a gap between the bolt and the part, and the external force is balanced by friction 

between the parts (Fig. 4). The magnitude of the force acting on the bolt 

  

𝑃 =
𝑘𝑃1

 f i z 
 

here: 𝑃1 - external force: f - coefficient of friction between parts: k= 1.4...2 - coefficient of 

caution: i - number of sections: z - number of bolts. 



 

168   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

A threaded bolt acts in tension and torsion, resulting in a calculation strength values  Рх=1/3P 

will be. The diameter of the bolt is determined by formula (1.6). Figure 4 

Figure 4 

2) There is no gap between the bolt and the part (Fig. 4). The shank of such bolts is tested for 

shear stress, and its diameter is determined as follows;  

𝑑 = √
4𝑃

𝜋𝑖𝑧[𝜏кес]
 

e). The acting force creates a bending moment in the rod member. When the surface of the part 

connecting to the surface of the nut is uneven (Fig. 1.4) or when using bolts made in the form of 

hooks with a head not specified in the standard, in addition to the tensile force, a bending 

moment is created. in its stem. Therefore, when calculating such bolts, in addition to the tensile 

force, it is necessary to pay attention to the bending moment. Tensile stress: 

б =
𝑃

(𝜋𝑑𝑘/4)
 

4) Stress created by bending moment: 𝜎эг =
𝑃𝑥

(0,1/𝑑1
2)

 If 𝑥 = 𝑑1  If 𝜎эг=𝑃/(0,1/𝑑1
2 

2) when the value of the angle a is small, the value of the stress in the bend is determined as 

follows, taking into account the additional deformation caused by this bending: 

𝜎эг =
𝑀

𝑊эг
≈ Е𝑑𝛼/2𝐼б 

 Here, :                                           M=EI/p, 𝜌 =
𝐼б

𝛼
 ; 𝑊эг =

𝐼

𝑑/2
  

The smallest value of these determined stresses is taken as the design bending stress. The general 

conditions for bolt strength are as follows: 

 б = б1 + бэг  ≤  [б] (8) 

  

  

  

 

 



 

169   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

 

 

 

 

  

 

 

 

 

Figure 5 

Calculations show that the ratio of these stresses 
бэг

б1
≈ 7.5 equals Therefore, the bending stress 

sharply reduces the strength of the bolt shank. Therefore, in such conditions it is better to use as 

few bolts as possible. 

Calculation of end connection bolts. Clamping connections are designed for fastening parts to 

shafts, axles, cylindrical columns and are formed by tightening the bolts themselves (Fig.6). 

 

Figure 6 

At one end of the lever prepared for this purpose there is a hole for the installation of a shaft, its 

diameter is easily adjusted to the shaft by a slot for the purpose, and by tightening the bolts it is 

compressed, and it is firmly fixed to the shaft. In this case, the moment of friction force arising 

between the surface of the hole and the surface of the shaft from the lever must be equal to or 

greater than the moment of external force (20% more), that is: 

f F d = 1,2 Q I 

As a result, the force generated on the surface of the terminal with the shaft:  

Ғ = 1,2 Q 1 / f d * 

where: f – friction coefficient; d – shaft diameter, – 1 – lever arm. If we assume that the lever 

with the terminal pin is fixed in a hinged position at point 0, then the condition for maintaining 

the equilibrium position of the terminal connection will be as follows, i.e. the sum of the 

moments about point O is obtained: 



 

170   Journal of Engineering, Mechanics and Architecture                      www. grnjournal.us  

 
 

𝑃𝐶𝑧 (𝛼 +
𝑑

2
) − 𝑃

𝑑

2
= 0 ** 

From here the value of the force 𝑃𝐶 required to pull the bolt is determined: 

𝑃𝐶 =
𝑃𝑑

(2𝛼 + 𝑑)𝑧
 

will be equal to Considering formulas :  

𝑃𝐶𝑍 = 𝑃 

Using formulas the amount of force required to tighten the bolt is determined as follows:  

𝑃𝐶 = 1.2 𝑄𝐼/𝑓𝑑𝑧      (9) 

Conclusion: Thus, to calculate the bolts of terminal connections, the force 𝑃𝐶 required to tighten 

the bolts is determined. Then their strength is calculated using the method given in b), i.e.  

𝜎экв =
1.3𝑃

𝜋𝑑𝑘
2

4

 ≤ [𝜎]     (10) 

The main advantage of clamp connections is that the lever can be positioned at any angle, 

creating a keyless connection, and is relatively easy to assemble and repair. The disadvantage is 

that these connections are unreliable (especially under the influence of variable forces).  

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