Engineering Mechanics & Design of Steel Structures: Rivets, Bolts and Welds

By Ashutosh Yadav|Updated : March 7th, 2022

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Structural Fasteners


The size of the rivet is the diameter of the shank.

  • Gross dia of rivet or dia of hole
    d' = d + 1.5 mm for d ≤ 25 mm
    and d' = d + 2.0 mm for d ≥ 25 mm
    where d = Nominal dia of rivet
    d' = Gross dia of rivet or dia of hole…
  • Unwins formula
    where, dmm = dia of rivet in mm
    tmm = thickness of plate in mm.

Bolted Joints

Bolts may be used in place of rivets for structure not subjected to vibrations. The following types of bolts are used in structures:

Black bolts

  • Hexagonal black bolts are commonly used in steel works.
  • They are made from low or medium carbon steels.
  • They are designated as black bolts M x d x l where d = diameter, and l = length of the bolts.

Precision and Semi Precision Bolts

  • They are also known as close tolerance bolts.
  • Sometimes to prevent excessive slip, close tolerance bolts are provided in holes of 0.15 to 0.2 mm oversize. This may cause difficulty in alignment and delay in the progress of work.
  • Types of Riveted and Bolted Joints
    There are two types of riveted or bolted joints.

(i) Lap joint

  • The lap joint is that in which the plates to be connected overlap each other.
  • The lap joint may have single-row, staggered or chain riveting.


(ii) Butt joint

  • The butt joint is that in which the plates to be connected butt against each other and the connection is made by providing a cover plate on one or both sides of joint.


  • The butt joint may have a single row or staggered or chain riveting.

Failure of Riveted/Bolted Joints

  1. By Tearing of Plate between rivets
    Strength of tearing per pitch length
    Pt = (p – d') t x ft
    where, ff = Permissible tensile stress in plates
    t = Thickness of plate
    d' = Dia of hole (gross dia of rivet)
    p = Pitch
  2. Strength of rivet in single shear image004
  3. Strength of rivet in double shear
    image005 where, fs = allowable shear stress in rivets
    d' = dia of hole.
  4. Failure due to bearing of crushing of rivet of plates
    Strength of rivet in bearing
    image006 where, fb = bearing strength of rivet.

Efficiency of Joints image007


Where, Ps = Strength of joint in shear

Pb = Strength of joint in bearing

Pt = Strength of joint in tearing

P = Strength of plate in tearing when no deduction has been made for rivet holes

= p. t. ft

  • Rivet value image009
  • Number of rivet, image010

IS 800: 1984 Recommendation

Maximum permissible stress in rivets & bolts


  • Rivet diameter, Pitch


Where t = thickness of thinner outside plate

Permissible Stresses


Max Permissible Deflections

  1. Max permissible horizontal and vertical deflection image014
  2. Max permissible deflection when supported elements are susceptible to cracking image015
  3. Max permissible deflection when supported elements are not susceptible to cracking image015


Arrangement of Rivets

(a) Chain Riveting


(b) Diamond Riveting


(c) Staggered Riveting


Eccentric Connections








Where, FDi = Direct force in ith rivet.

FTi = Force in ith rivet due to torsional moment

ri = Distance of ith rivet from CG

Ai = Area of ith rivet image024

FDi = Always acts in the direction of applied load P.

FTi = Always acts perpendicular to the line joining CG of rivet group and the rivet under consideration.

Fri = Resultant force in ith rivet.


Minimum size of weld

It depends upon thickness of thicker plate


Max clear spacing between effective length of weld in compression zone = 12t or 200 mm (minimum). In tension zone = 16 t or 200 mm (minimum)

  • Slot weld




  • Slide fillet weld


(a) image031

(b) image032 to make stress distribution uniform

(c) if b1 > 16t use end fillet weld.

Welded Connection

  • Permissible Stresses

(a) Tensions and compression on section through the throat of butt weld = 150 N/mm2

(b) Shear on section through the throat of butt of fillet weld =108 N/mm2 ≅ 100 N/mm2
Throat thickness t = k x size of weld

  • Butt-welded Joint Loaded Eccentrically

Let the thickness of weld throat = t, and length of weld = d

  • Shear stress at weld, image033

Where t = thickness of weld throat and d = length of weld.


  • Tensile or compressive stress due to bending at extreme fibre,


For the safety of joint the interaction equation.


  • Equivalency Method

image037 (based on max distortion energy theory)

Permissible bending stress for flanged section = 165 N/mm2 = 0.67fy

For solid section image038 permissible bending stress is 185 N/mm2

Fillet-Welded Joint Loaded Eccentrically

There can be two cases:

  • Load not lying in the plane of the weld
  • Load lying in the plane of the weld

(i) Load not lying in the plane of the weld:

  • Let thickness of weld throat = t and total length of weld = 2 x d
  • Vertical shear stress at weld,
  • Horizontal shear stress due to bending at extreme fibre,
  • Resultant stress, image041
  • The value of pr should not exceed the permissible shear stress pq (= 108 MPa) in the weld.


  • For design of this connection, the depth of weld may be estimated approximately by

(ii) Load lying in the plane of the weld: Consider a bracket connection to the flange of a column by a fillet weld as shown in figure

  • Vertical shear stress at weld, image044


image045 the length of weld and t = thickness of the throat

  • Torsional stress due to moment, at any point in the weld, image046


T = torsional moment = W x e

r = distance of the point from cg of weld section

Ip = polar moment of inertia of the weld group = lx + ly


  • The resultant stress, image047
  • For safety, image048 permissible stress in fillet weld, i.e. 108 MPa.
  • The resultant stress pr will be maximum at a point where r is maximum and q is minimum. 


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