Design of Riveted Joints | Design of Machine Elements - Mechanical Engineering PDF Download

Strength of riveted joint

The strength of a riveted joint is assessed by considering every possible failure path through the joint. Because rivets are arranged periodically, analysis is usually carried out for one pitch length of the plate. A single-riveted joint under direct tensile load may fail in one of several distinct ways; the common failure modes are listed and analysed below.

Failure modes of riveted joints

a) Tearing of the plate along the row

If the applied tensile force is large, the plate may tear along the line of rivet holes. The available net cross-section per pitch equals the gross pitch minus one hole diameter, multiplied by the plate thickness. The maximum permissible load to prevent tearing along the row is

P₁ = s_t (p - d) t

where s_t is the allowable tensile stress of the plate material, p is the pitch, d is the rivet-hole diameter, and t is the plate thickness.

b) Shearing of the rivet

The rivet shank may fail in shear on one or more shear planes depending on the joint configuration. For a single shear plane the shear area of the rivet shank is the circular cross-section.

P₂ = s_s × (π d² / 4)

where s_s is the allowable shear stress of the rivet material. For double shear the shear capacity is twice the single-shear value (i.e. 2 × s_s × (π d² /4)).

c) Crushing (bearing) of rivet or plate

High bearing (contact) stress between the rivet and the plate may crush the rivet or indent the plate at the hole. With the simplifying assumption of uniform bearing stress over the projected bearing area, the maximum allowable load in bearing is

P₃ = s_c d t

where s_c is the allowable bearing (crushing) stress between rivet and plate material.

d) Tearing of the plate at the margin (edge)

If the edge margin (distance from centre of rivet hole to plate edge) is insufficient, the plate may tear out from the edge. A commonly used minimum margin for riveted connections is

m = 1.5 d

This margin reduces the risk of failure of the plate between the hole and the edge under tensile loading.

Strength and efficiency of riveted joints

The strength of the riveted joint (per pitch) is governed by the weakest of the above failure modes. Therefore the permissible tensile load on the joint per pitch is the minimum of the mode values:

P_joint = min { P₁, P₂, P₃ }

The strength of a solid plate of the same gross width (equal to pitch p) is S_t p t, where S_t is the allowable tensile stress of the plate material.

The efficiency (η) of the riveted joint is defined as the ratio of the strength of the riveted joint to the strength of the corresponding solid plate:

η = P_joint / (S_t p t)

Failure considerations in double and multiple riveted joints

In double- or triple-riveted joints, additional failure patterns occur because there are multiple rows of rivets. The outer row may cause tearing similar to the single-rivet case, but inner rows introduce combined failure sequences: for an inner-row tear to occur the outer-row rivets must have failed (by shear or crushing). For example, in a double-riveted joint the load that will cause tearing at the second row (inner row) while allowing the first-row rivets to fail is

P₄ = s_t (p - d) t + min { P₂, P₃ }

Other possible modes in multiple-row joints are

• shearing of rivets in all rows,
• crushing (bearing) of rivets in all rows,
• combination of shear in some rows and crushing in others.

The joint efficiency must be obtained by considering every possible mode and selecting the lowest ultimate permissible load (i.e. the weakest failure path).

Design of riveted joints - main parameters

The key geometric parameters in rivet-joint design are the rivet-hole diameter d, the pitch p and the edge margin m. Design proceeds by choosing these so that no failure mode is exceeded under the working load and relevant safety/allowable stresses.

Diameter of the hole (d)

For thicker plates, empirical or semi-empirical relations are commonly used. Unwin's formula gives the recommended rivet diameter when the plate thickness is large:

d = 6 √t mm

when the plate thickness t is more than 8 mm. If the thickness is less than or equal to 8 mm, the rivet diameter is usually chosen by equating the crushing (bearing) strength to the shear strength so that neither mode dominates unnecessarily. For a rivet in single-shear with uniform bearing the equating condition is

s_c d t = s_s (π d² / 4)

From this relation a value of d can be obtained (note that the resulting expression may be simplified to an expression of the form d ∝ t when material allowable stresses are known). Always ensure that d ≥ t and that chosen diameters conform to standard sizes given in codes (e.g. IS:1928).

Pitch (p)

Pitch is selected so that the tearing strength of the plate equals (or exceeds) the shear strength provided by the rivets in the pitch length. For a particular joint arrangement (for example a double-riveted lap joint) the tearing strength per pitch is s_t (p - d) t. The total shear resistance offered by the rivets across the pitch depends on the number of rivets sharing the load and the number of shear planes per rivet; equate these to determine p. Additionally, practical limits apply - for example, there must be sufficient spacing to accommodate rivet heads and bucked ends, hence

p ≥ 2 d

is commonly enforced for lap joints.

Edge margin (m)

An adequate margin prevents edge tearing. A commonly used rule is

m = 1.5 d

Design checks, standards and boiler joints

Designers must comply with relevant standards and regulations. Standard rivet-hole and rivet sizes are listed in national/international codes (for example, IS:1928). When designing boiler joints or pressure-vessel-type joints the Indian Boiler Regulations (I.B.R.) (or the relevant statutory regulation) must be followed. A recommended distance for rivet pitch from the edge or for certain lap details used in boiler practice is sometimes expressed by empirical relations; for example, a commonly used value for a particular dimension related to boiler practice is

p_b ≈ 0.33 p + 0.67 d mm

Design procedure - concise ordered steps

1. Determine the working tensile load per pitch to be transmitted by the joint.
2. Choose an initial rivet diameter d (use Unwin's rule if t > 8 mm or an initial standard diameter from code tables).
3. Choose a preliminary pitch p satisfying practical limits (p ≥ 2d) and the required strength; calculate P₁, P₂, P₃ for the chosen d, p and t.
4. Compute P_joint = min{P₁,P₂,P₃} and joint efficiency η = P_joint / (S_t p t).
5. Verify edge margin m = 1.5 d (or as required by code). Adjust d and p and repeat calculations until all strength and serviceability criteria and code limits are satisfied.
6. Check secondary requirements for the application (e.g. corrosion allowance, fatigue considerations, boiler regulations) and make final adjustments.

Worked illustrative example (symbolic)

The following is a symbolic illustration of selecting rivet diameter by equating bearing and shear strength for a single shear rivet when Unwin's formula is not used.

Assume allowable stresses s_c and s_s are known and plate thickness is t.

s_c d t = s_s (π d² / 4)

Divide both sides by d:

s_c t = s_s (π d / 4)

Solve for d:

d = (4 s_c t) / (π s_s)

Round d up to the nearest standard size and ensure d ≥ t. Then determine pitch p from tearing vs rivet shear condition and check all failure modes as described earlier.

Practical notes and applications

• Riveted joints remain important in historical designs and in specific applications where welding is impractical; understanding failure modes helps in retrofitting and inspection.
• Fatigue and shear-out under repeated loading require larger margins and careful choice of spacing and rivet quality; consult relevant codes for fatigue design details.
• Codes specify standard rivet diameters, allowable stresses for rivets and plates, hole clearances, and inspection criteria; always follow the applicable standard for safety-critical work such as boilers and pressure vessels.

Summary

Design of riveted joints requires systematic evaluation of the principal failure modes: plate tearing, rivet shear, rivet/plate bearing (crushing) and edge tearing. The designer selects rivet diameter d, pitch p and margin m so that the weakest permissible load of the joint exceeds the required load with suitable factor of safety and conforms to codes (for example IS:1928 and the Indian Boiler Regulations where applicable). Use Unwin's rule for initial rivet diameter when t > 8 mm and always check all modes to find the governing (minimum) capacity before declaring the design acceptable.