Note 03 - Bolted and Riveted Joints Loaded in Shear_220628_090232.pdf

1. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 1 of 21
ME451
Note 03
Rivets

2. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 2 of 21
ME451
Note 03
Rivets

3. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 3 of 21
ME451
Note 03
The reasons for choosing rivets over threaded fasteners are the following
• Rivets will not shake loose.
• Can join difficult to weld parts
• They are cheap, especially in assembly time.
• They are lightweight.
However, rivets cannot provide as strong an attachment as a threaded fastener of the same diameter. Also, rivets do not allow any disassembly of the joint.
Rivets must be spaced neither too close nor too far apart. The minimum rivet spacing, center to center, is usually taken as three rivet diameters for structural
steelwork.

4. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 4 of 21
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Note 03
The four different modes of failure primarily cause failure due to a shear force. Bending of a member, shearing of the rivet, tensile failure of a member, and the
bearing of the rivet on a member or the bearing of a member on the rivet
failure by bending of
the rivet or of the
riveted members.
failure of the rivet
by pure shear
Rupture of one of the
connected member or
plates by pure tension
failure by crushing of
the rivet or plate

5. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 5 of 21
ME451
Note 03
Bending of a member
To avoid this failure, the following should be valid
𝜎 =
𝑀 𝑐
𝐼
=
𝑃
𝐿𝑔
2
𝑐
𝐼
=
𝑆𝑦𝑗
𝑛𝑠
where
𝐿𝑔 = length of the grip, m.
(𝑆𝑦)𝑗
= yield strength of weakest member, Pa.

6. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 6 of 21
ME451
Note 03
Shear of rivets
To avoid this failure, the following should be valid
𝜏 =
𝑃
𝐴
=
4𝑃
𝜋𝑑𝑐
2
=
𝑆𝑠𝑦
𝑛𝑠
where
𝑑𝑐 = crest diameter, m.
𝑆𝑠𝑦 = rivet shear yield strength, Pa.

7. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 7 of 21
ME451
Note 03
Tensile failure of a member
To avoid this failure, the following should be valid
𝜎 =
𝑃
𝐴
=
𝑃
(𝑏 − 𝑁𝑟𝑑𝑐)𝑡𝑚
=
𝑆𝑦𝑗
𝑛𝑠
where
𝑏 = width of member, m.
𝑁𝑟 = number of rivets in the width of member.
𝑡𝑚= thickness of the thinnest member.

8. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 8 of 21
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Note 03
Compressive bearing failure.
To avoid this failure, the following should be valid
𝜎 =
𝑃
𝐴
=
𝑃
𝑑𝑐𝑡𝑚
=
𝑆𝑦𝑗
𝑛𝑠

9. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 9 of 21
ME451
Note 03
Threaded and rivets are used in groups, and the torsional shear of the group must be considered as a failure mode.

10. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 10 of 21
ME451
Note 03

11. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 11 of 21
ME451
Note 03
Threaded and rivets are used in groups, and the torsional shear of the group must be considered as a failure mode. The resulting shear stress acting on the rivet is
the vectorial sum of the direct and torsional shear stresses.

12. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 12 of 21
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Note 03
The centroid of the bolt arrangement is found from
𝑥̅ =
∑ 𝐴𝑖𝑥𝑖
𝑁
𝑖=1
∑ 𝐴𝑖
𝑁
𝑖=1
𝑦
̅ =
∑ 𝐴𝑖𝑦𝑖
𝑁
𝑖=1
∑ 𝐴𝑖
𝑁
𝑖=1
The moment of inertia 𝐽 = ∑ 𝐴𝑖 𝑟𝑖
2
𝑁
𝑖=1

13. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 13 of 21
ME451
Note 03
The resulting shear stress acting on the rivet is the vectorial sum of the direct and torsional
shear stresses 𝜏 = 𝜏𝑏 + 𝜏𝑡 = 𝜏′
+ 𝜏′′
where 𝜏𝑏 = 𝜏′
=
𝑃
𝑁𝐴
shear stress of rivet, or direct shear.
𝜏𝑡 = 𝜏′′
=
𝑇𝑟
𝐽
shear stress of rivet due to torsional loading.
The moment of inertia 𝐽 = ∑ 𝐴𝑖 𝑟𝑖
2
𝑁
𝑖=1

14. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 14 of 21
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Note 03
Example
The riveted member is fastened to a beam, and an eccentric load is applied. Rivets 𝐴 and 𝐶 have 5/8 in
diameter, and rivets 𝐵 and 𝐷 have 7/8 in diameter. Find
a) The centroid of the rivet assembly
b) Direct and resultant shear stresses acting on each rivet
c) Safety factor guarding against shear of the rivet
Assume that the yield stress of the rivet is 85 ksi.

15. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 15 of 21
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Note 03

16. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 16 of 21
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Example
A plate is riveted as shown. The three rivets have a 5/8 in diameter and carry
the load and moment resulting from the external load of 1950 lb. The yield
strengths of the materials are 𝑆𝑦,𝑟𝑖𝑣𝑒𝑡 = 85 kpsi and 𝑆𝑦,𝑝𝑙𝑎𝑡𝑒 = 50 kpsi.
Calculate the safety factors for
a) Shear of rivet
b) Bearing of rivet
c) Bearing of plate
d) Bending of plate

17. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 17 of 21
ME451
Note 03

18. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 18 of 21
ME451
Note 03

19. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 19 of 21
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Note 03
Example
Find the value of 𝑃 for the joint shown based on working stress of 15,000 psi in shear. All four rivets are
identical with a diameter of 0.75".

20. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 20 of 21
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Note 03
Example
The figure shows a vertically loaded bracket attached to a fixed member by three identical
bolts. Select three SAE class 9.8 steel bolts to withstand the loaded configuration show.
Consider shear plus tension in each bolt.

21. Screws, Fasteners and Connections Bolted and Riveted Joints Loaded in Shear
Bolted and Riveted Joints Loaded in Shear Page 21 of 21
ME451
Note 03