Design of Connections

Riveting

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, d_mm = dia of rivet in mm
t_mm= 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

By Tearing of Plate between rivets
Strength of tearing per pitch length
P_t = (p – d') t x f_twhere, f_f = Permissible tensile stress in plates
t = Thickness of plate
d' = Dia of hole (gross dia of rivet)
p = Pitch
Strength of rivet in single shear
Strength of rivet in double shear
where, f_s = allowable shear stress in rivets
d' = dia of hole.
Failure due to bearing of crushing of rivet of plates
Strength of rivet in bearing
where, f_b = bearing strength of rivet.

Efficiency of Joints

Where, P_s = Strength of joint in shear

P_b = Strength of joint in bearing

P_t = Strength of joint in tearing

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

= p. t. f_t

Rivet value
Number of rivet,

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

Max permissible horizontal and vertical deflection
Max permissible deflection when supported elements are susceptible to cracking
Max permissible deflection when supported elements are not susceptible to cracking

Arrangement of Rivets

(a) Chain Riveting

(b) Diamond Riveting

Eccentric Connections

Where, F_Di = Direct force in i^th rivet.

F_Ti = Force in i^th rivet due to torsional moment

r_i = Distance of i^th rivet from CG

A_i = Area of i^th rivet

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

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

F_ri = Resultant force in i^th 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)

(b) to make stress distribution uniform

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/mm²Throat 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,

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

(based on max distortion energy theory)

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

For solid section 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,
The value of p_r should not exceed the permissible shear stress p_q (= 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,

where,

the length of weld and t = thickness of the throat

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

where,

T = torsional moment = W x e

r = distance of the point from cg of weld section

I_p = polar moment of inertia of the weld group = l_x + l_y

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