If the working stress in bearing in power driven rivets is 300 N/mm² and a double riveted double cover butt joint is used to connect plates of 12 mm thick, then the strength of rivet in bearing is
(Given: The nominal diameter of rivet = 22 mm)

Question

If the working stress in bearing in power driven rivets is 300 N/mm² and a double riveted double cover butt joint is used to connect plates of 12 mm thick, then the strength of rivet in bearing is

(Given: The nominal diameter of rivet = 22 mm)

Prepp Team · Accepted Answer

Understanding Rivet Bearing Strength in Structural Joints

This question asks us to calculate the bearing strength of a single power-driven rivet used in a double riveted double cover butt joint. Bearing strength is one of the critical failure modes for a riveted connection, occurring when the plate material crushes or tears around the rivet hole due to excessive pressure from the rivet.

Key Parameters from the Question

Type of joint: Double riveted double cover butt joint
Main plate thickness ($t$): 12 mm
Working stress in bearing ($\sigma_b$): 300 N/mm<sup>2</sup> (for power driven rivets)
Nominal diameter of rivet ($d$): 22 mm

Calculating the Effective Diameter of the Rivet

For rivets with a nominal diameter of 25 mm or less, the gross diameter (or hole diameter), which is used in strength calculations, is taken as the nominal diameter plus 1.5 mm. This accounts for the hole clearance and the expansion of the rivet during driving.

Nominal diameter, $d = 22$ mm

Gross diameter, $D = d + 1.5 \, \text{mm} = 22 \, \text{mm} + 1.5 \, \text{mm} = 23.5 \, \text{mm}$

Determining Effective Thickness for Bearing

In a double cover butt joint, the rivet bears against the main plate and against the two cover plates combined. The bearing strength is limited by the thinner of these sections. The effective thickness for bearing calculation is the minimum of the main plate thickness ($t$) and the sum of the thicknesses of the two cover plates ($2t_c$). However, the question only provides the main plate thickness (12 mm) and not the cover plate thickness. Assuming the cover plates are adequately thick (e.g., each cover plate is at least half the main plate thickness, making their combined thickness at least equal to the main plate thickness), the bearing on the main plate often governs. Therefore, we will use the main plate thickness as the effective thickness ($t_{eff}$) for the bearing calculation in this case.

Effective thickness for bearing, $t_{eff} = 12$ mm

Formula for Bearing Strength of a Rivet

The bearing strength of a single rivet is calculated using the following formula:

$$ P_b = \sigma_b \times D \times t_{eff} $$

Where:

$P_b$ is the bearing strength of the rivet.
$\sigma_b$ is the working stress in bearing.
$D$ is the gross diameter of the rivet.
$t_{eff}$ is the effective thickness of the plate in bearing.

Step-by-Step Calculation

Substitute the known values into the formula:

$P_b = 300 \, \text{N/mm}^2 \times 23.5 \, \text{mm} \times 12 \, \text{mm}$

$P_b = 300 \times 23.5 \times 12 \, \text{N}$

$P_b = 84600 \, \text{N}$

To convert Newtons (N) to KiloNewtons (kN), divide by 1000:

$P_b = \frac{84600}{1000} \, \text{kN}$

$P_b = 84.6 \, \text{kN}$

Thus, the strength of the rivet in bearing is 84.6 kN.

Comparison with Options

Let's compare our calculated value with the given options:

Option 1: 84.6 kN
Option 2: 54.6 kN
Option 3: 72.6 kN
Option 4: 68.4 kN

Our calculated bearing strength of 84.6 kN matches Option 1.

Parameter	Value	Unit
Nominal Diameter (d)	22	mm
Gross Diameter (D)	23.5	mm
Plate Thickness (t)	12	mm
Effective Thickness for Bearing ($t_{eff}$)	12	mm
Bearing Stress ($\sigma_b$)	300	N/mm<sup>2</sup>
Bearing Strength ($P_b$)	84600	N
Bearing Strength ($P_b$)	84.6	kN

The calculation confirms that the bearing strength of a single rivet under the given conditions is 84.6 kN.

Revision Table: Riveted Joint Strength

Failure Mode	Description	Relevant Parameters	Formula for Single Rivet (or Plate)
Shearing of Rivet	Rivet shank shears off. Can be single shear or double shear.	Gross diameter (D), Permissible shear stress ($\tau_v$), Number of shear planes (n)	$P_s = n \times \frac{\pi}{4}D^2 \times \tau_v$
Bearing of Rivet/Plate	Crushing of plate or rivet material at contact surface.	Gross diameter (D), Plate thickness (t), Permissible bearing stress ($\sigma_b$)	$P_b = D \times t \times \sigma_b$
Tearing of Plate	Plate tears across a row of rivets.	Plate width (b), Hole diameter (D), Number of rivets in the row (n), Permissible tensile stress ($\sigma_t$)	$P_t = (b - nD) \times t \times \sigma_t$ (for gross area) or considering net area and stress concentration. For a row: $(p - D) \times t \times \sigma_t$, where p is pitch.

The strength of the joint per pitch length or the total strength of the joint is the minimum of the strengths considering all potential failure modes.

Additional Information: Double Cover Butt Joint

A double cover butt joint is a type of riveted or bolted connection used to join two plates end-to-end. The ends of the main plates are butted against each other, and cover plates are placed on both the top and bottom surfaces, spanning the joint. Rivets or bolts then pass through the cover plates and the main plates.

Advantages:
- Provides a symmetrical connection, reducing bending stress on the rivets.
- Higher efficiency can be achieved compared to lap joints or single cover butt joints, especially in tension.
- The load is transferred more directly across the joint.
"Double Riveted": This term refers to the arrangement of rivets. In a double riveted joint, there are two rows of rivets connecting the plates (either in chain riveting or zig-zag riveting pattern) on each side of the butt line. The strength of the joint depends on the strength of a single rivet (minimum of shear and bearing strength) multiplied by the number of rivets in the critical failure pattern (often the number of rivets in a pitch length or the total number of rivets, depending on the failure mode being considered). However, the question specifically asked for the strength of *a* rivet in bearing.
Power Driven Rivets: These are rivets installed using pneumatic or hydraulic riveting hammers. They are typically hot-driven, meaning the rivet is heated before being inserted and hammered, which helps fill the hole better and provides clamping force upon cooling. Design codes often permit higher working stresses for power-driven rivets compared to hand-driven rivets.

Understanding the type of joint and the method of riveting is crucial as it affects the permissible stresses and the calculation procedures according to relevant design codes (like IS 800 for steel structures in India).

Prepp Team · Answer

54.6 kN

Prepp Team · Answer

72.6 kN

Prepp Team · Answer

68.4kN