Efficiency of Joint MCQ Quiz - Objective Question with Answer for Efficiency of Joint - Download Free PDF

Concept:

In a riveted joint, the tensile resistance of the plate is determined based on the net cross-sectional area left between rivet holes.

\( P_t = (\text{Net Area}) \times \sigma_t \)

Net area between two rivets = \( (p - d) \cdot t \)

Given:

\( p \) = pitch of rivets (mm)

\( d \) = diameter of rivet hole (mm)

\( t \) = thickness of plate (mm)

\( \sigma_t \) = permissible tensile stress of plate material (N/mm²)

Calculation:

\( P_t = (p - d) \times t \times \sigma_t \)

Concept:

The efficiency of a riveted joint is the ratio of the strength of the joint (minimum of tearing, shearing, or crushing strength) to the strength of the solid plate without holes.

Given:

Plate thickness, t = 10 mm

Rivet diameter, d = 20 mm

Pitch of rivets, p = 50 mm

Permissible tensile stress in plate = 150 MPa

Permissible shear stress in rivet = 100 MPa

Permissible crushing stress in rivet = 200 MPa

π = 3.14

Calculation:

Tearing strength of plate, \( P_t = (p - d) \times t \times \sigma_t = (50 - 20) \times 10 \times 150 = 45000~N \)

Shearing strength of rivet, \( P_s = \frac{\pi}{4} \times d^2 \times \tau = \frac{3.14}{4} \times 20^2 \times 100 = 31400~N \)

Crushing strength of rivet, \( P_c = d \times t \times \sigma_c = 20 \times 10 \times 200 = 40000~N \)

Strength of joint is minimum of tearing, shearing and crushing: \( P = \min(45000, 31400, 40000) = 31400~N \)

Strength of solid plate (without rivet hole), \( P_{solid} = p \times t \times \sigma_t = 50 \times 10 \times 150 = 75000~N \)

Efficiency of the joint, \( \eta = \frac{P}{P_{solid}} \times 100 = \frac{31400}{75000} \times 100 = 41.86\% \)

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{η _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{η _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore η = \frac{{p - d}}{p}\)

if p1 is the pitch of the rivets for the lap joint and d is the diameter of the rivet hole, then the above equation will be written as:

\(\therefore η = \frac{{p_1 - d}}{p_1}\)

Concept:

Tensile Stresses in the main plates might result in tearing of the main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as the tearing strength or tearing value of the plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{η _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{η _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore η = \frac{{p - d}}{p}\)

Calculation:

Given: d/p  = 0.3,

Tearing efficiency, 

\(η =1-\frac{d}{p}\)

⇒ η = 1 - 0.3

⇒ η = 0.7

⇒ η = 70%

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.75

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.75 \Rightarrow \frac{d}{p} = 0.25\)

Concept:

Riveted joint:

• The permanent joining of parts with the help of rivets is called a riveted joint.
• Rivets are cylindrical-shaped metal body used to leakproof the joining of dissimilar metals.
• When two pieces of sheet joint with the help of riveted joint such that one sheet overlaps the other one then this type of joint is called lap joint.

The efficiency of the riveted joint is defined as the ratio of the strength of the plate in an unpunched condition.

\(\eta = \frac{{Strength\;of\;riveted\;joint}}{{Strength\;of\;unriveted\;solid\;plate}}\)

As the strength of the riveted joint depends on the tearing strength, shearing strength or crushing strength of the joint, the efficiency can be tearing efficiency, shearing efficiency, and crushing efficiency.

The efficiency of the riveted joint,

\(\eta = \frac{{Lowest\;of\;{P_s},\;{P_t}\;and\;{P_c}}}{P}\)

Where P_s = Shearing resistance, P_t = Tearing resistance, P_c = Crushing resistance, P = Strength of plate.

Calculation:

Given:

P_s = 20 kN, P_c = 30 kN, P_t = 35 kN, P = 25 kN. 

Among These P_s is the Lowest

∴ The efficiency of the riveted joint is given by:

\(\eta = \frac{P_s}{P} = \frac{20}{25} = 0.8\)

∴ The efficiency of the rivet joint is 0.8.

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p} \times t\times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.60

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.6 \Rightarrow \frac{d}{p} = 0.4\)

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.50

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.5 \Rightarrow \frac{d}{p} = 0.5\)

Concept:

In a riveted joint, the tensile resistance of the plate is determined based on the net cross-sectional area left between rivet holes.

\( P_t = (\text{Net Area}) \times \sigma_t \)

Net area between two rivets = \( (p - d) \cdot t \)

Given:

\( p \) = pitch of rivets (mm)

\( d \) = diameter of rivet hole (mm)

\( t \) = thickness of plate (mm)

\( \sigma_t \) = permissible tensile stress of plate material (N/mm²)

Calculation:

\( P_t = (p - d) \times t \times \sigma_t \)

Concept:

The efficiency of a riveted joint is the ratio of the strength of the joint (minimum of tearing, shearing, or crushing strength) to the strength of the solid plate without holes.

Given:

Plate thickness, t = 10 mm

Rivet diameter, d = 20 mm

Pitch of rivets, p = 50 mm

Permissible tensile stress in plate = 150 MPa

Permissible shear stress in rivet = 100 MPa

Permissible crushing stress in rivet = 200 MPa

π = 3.14

Calculation:

Tearing strength of plate, \( P_t = (p - d) \times t \times \sigma_t = (50 - 20) \times 10 \times 150 = 45000~N \)

Shearing strength of rivet, \( P_s = \frac{\pi}{4} \times d^2 \times \tau = \frac{3.14}{4} \times 20^2 \times 100 = 31400~N \)

Crushing strength of rivet, \( P_c = d \times t \times \sigma_c = 20 \times 10 \times 200 = 40000~N \)

Strength of joint is minimum of tearing, shearing and crushing: \( P = \min(45000, 31400, 40000) = 31400~N \)

Strength of solid plate (without rivet hole), \( P_{solid} = p \times t \times \sigma_t = 50 \times 10 \times 150 = 75000~N \)

Efficiency of the joint, \( \eta = \frac{P}{P_{solid}} \times 100 = \frac{31400}{75000} \times 100 = 41.86\% \)

Concept:

Riveted joint:

• The permanent joining of parts with the help of rivets is called a riveted joint.
• Rivets are cylindrical-shaped metal body used to leakproof the joining of dissimilar metals.
• When two pieces of sheet joint with the help of riveted joint such that one sheet overlaps the other one then this type of joint is called lap joint.

The efficiency of the riveted joint is defined as the ratio of the strength of the plate in an unpunched condition.

\(\eta = \frac{{Strength\;of\;riveted\;joint}}{{Strength\;of\;unriveted\;solid\;plate}}\)

As the strength of the riveted joint depends on the tearing strength, shearing strength or crushing strength of the joint, the efficiency can be tearing efficiency, shearing efficiency, and crushing efficiency.

The efficiency of the riveted joint,

\(\eta = \frac{{Lowest\;of\;{P_s},\;{P_t}\;and\;{P_c}}}{P}\)

Where P_s = Shearing resistance, P_t = Tearing resistance, P_c = Crushing resistance, P = Strength of plate.

Calculation:

Given:

P_s = 20 kN, P_c = 30 kN, P_t = 35 kN, P = 25 kN. 

Among These P_s is the Lowest

∴ The efficiency of the riveted joint is given by:

\(\eta = \frac{P_s}{P} = \frac{20}{25} = 0.8\)

∴ The efficiency of the rivet joint is 0.8.

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p} \times t\times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.60

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.6 \Rightarrow \frac{d}{p} = 0.4\)

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.50

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.5 \Rightarrow \frac{d}{p} = 0.5\)

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{η _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{η _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore η = \frac{{p - d}}{p}\)

Calculation: \(\frac dp=0.5\)

\(η = \frac{{p - d}}{p}\)

\(η =1 - \frac{d}{p} \Rightarrowη =1-0.5\)

η = 50%

Concept:

Tensile Stresses in the main plates might result in tearing of main plate or cover plate across a row of the bolt.

The resistance offered by the plate against tearing is known as tearing strength or tearing value of plate.

Tearing efficiency of joints is given by,

\(\begin{array}{*{20}{c}} {{\eta _t} = \frac{\rm{Tearing\;strength}}{{\rm Strength\;of\;solid\;plate}}}\\ {{\eta _t} = \frac{{\left( {p - d} \right) \times t \times {\sigma _t}}}{{{p_t} \times {\sigma _t}}} = \frac{{p - d}}{p}} \end{array}\)

\(\therefore \eta = \frac{{p - d}}{p}\)

Calculation:

Given that tearing efficiency = 0.75

 \(\eta = \frac{{p - d}}{p}\)

\(1 - \frac{d}{p} = 0.75 \Rightarrow \frac{d}{p} = 0.25\)