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What is the formula used to calculate average normal stress?
What is the formula used to calculate average normal stress?
Which type of stress occurs when a force is applied normally to the surface of a material?
Which type of stress occurs when a force is applied normally to the surface of a material?
What is shearing stress primarily caused by?
What is shearing stress primarily caused by?
Which type of stress refers to the contact pressure between two surfaces of bodies?
Which type of stress refers to the contact pressure between two surfaces of bodies?
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In the context of stress, what does tensile stress do to a material?
In the context of stress, what does tensile stress do to a material?
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Which of the following is NOT a type of normal stress?
Which of the following is NOT a type of normal stress?
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When calculating the maximum average normal stress in a loading scenario, which material property is essential?
When calculating the maximum average normal stress in a loading scenario, which material property is essential?
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What effect does compressive stress have on a material?
What effect does compressive stress have on a material?
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What is the maximum load P that can be applied if the working stress for shear in the rivet is 14 ksi and the working stress for bearing in the plate is 18 ksi?
What is the maximum load P that can be applied if the working stress for shear in the rivet is 14 ksi and the working stress for bearing in the plate is 18 ksi?
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In a thin-walled cylinder under internal pressure, what is the formula for tangential stress, σt?
In a thin-walled cylinder under internal pressure, what is the formula for tangential stress, σt?
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What kind of stresses are developed across the sections of a tank carrying fluid or gas under pressure?
What kind of stresses are developed across the sections of a tank carrying fluid or gas under pressure?
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If a tank has an external pressure $p_o$ and an internal pressure $p_i$, how does the tangential stress theoretically change?
If a tank has an external pressure $p_o$ and an internal pressure $p_i$, how does the tangential stress theoretically change?
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What is the relationship between the force acting at the rear of a tank and the total longitudinal stress on the wall?
What is the relationship between the force acting at the rear of a tank and the total longitudinal stress on the wall?
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What happens to the maximum load P if one rivet experiences a shearing force greater than the allowed 14 ksi?
What happens to the maximum load P if one rivet experiences a shearing force greater than the allowed 14 ksi?
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Which condition contributes to the tangential stress on the walls of a cylindrical tank?
Which condition contributes to the tangential stress on the walls of a cylindrical tank?
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What is necessary for a thin-walled cylinder to avoid bursting under internal pressure?
What is necessary for a thin-walled cylinder to avoid bursting under internal pressure?
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What is the maximum average normal stress represented by the formula $\sigma = \frac{P_{BC}}{A}$ where $P_{BC}$ equals $30 (10^3)$ N and $A$ equals $(0.035 m)(0.010 m)$?
What is the maximum average normal stress represented by the formula $\sigma = \frac{P_{BC}}{A}$ where $P_{BC}$ equals $30 (10^3)$ N and $A$ equals $(0.035 m)(0.010 m)$?
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Given a vertical force of 3 kN applied to member AC, which statements correctly describe the forces acting at support C?
Given a vertical force of 3 kN applied to member AC, which statements correctly describe the forces acting at support C?
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What is the cross-sectional area of the tie rod AB mentioned in the scenario?
What is the cross-sectional area of the tie rod AB mentioned in the scenario?
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How do you calculate the average compressive stress at the support C?
How do you calculate the average compressive stress at the support C?
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In the given problem, if the area at support C is 650 mm², what impact does this have on the compressive stress?
In the given problem, if the area at support C is 650 mm², what impact does this have on the compressive stress?
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Which of these elements is necessary to find the position x of the force to balance stresses in the rod and support?
Which of these elements is necessary to find the position x of the force to balance stresses in the rod and support?
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What contributes to the tensile stress in the tie rod AB when under load?
What contributes to the tensile stress in the tie rod AB when under load?
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Which conclusion can be drawn about the forces acting on member AC?
Which conclusion can be drawn about the forces acting on member AC?
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What is the definition of average shear stress?
What is the definition of average shear stress?
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If a 20-mm-diameter pin has a shear force of 12.5 kN, what is the shear stress at pin A?
If a 20-mm-diameter pin has a shear force of 12.5 kN, what is the shear stress at pin A?
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In which situation would single shear stress occur?
In which situation would single shear stress occur?
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What is the average compressive stress along the areas defined by AB and BC if a compressive force of 600 lb is applied?
What is the average compressive stress along the areas defined by AB and BC if a compressive force of 600 lb is applied?
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If the average shear stress is calculated using a total shear force of 20 kN and sheared area of 1000 mm², what would be its value?
If the average shear stress is calculated using a total shear force of 20 kN and sheared area of 1000 mm², what would be its value?
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Which type of shear is defined as occurring when loads cause adjacent sections to slide past each other with tangential stress?
Which type of shear is defined as occurring when loads cause adjacent sections to slide past each other with tangential stress?
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What is a key characteristic of double shear compared to single shear?
What is a key characteristic of double shear compared to single shear?
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What is the formula used to calculate the reaction force at point A if forces of 7.50 kN and 20 kN act at a certain angle?
What is the formula used to calculate the reaction force at point A if forces of 7.50 kN and 20 kN act at a certain angle?
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What is the formula for calculating tangential stress in a cylindrical pressure vessel?
What is the formula for calculating tangential stress in a cylindrical pressure vessel?
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If an internal pressure of 4.5 MN/m² is applied to a cylindrical steel pressure vessel with a 400 mm diameter and 20 mm thickness, what is the calculated tangential stress?
If an internal pressure of 4.5 MN/m² is applied to a cylindrical steel pressure vessel with a 400 mm diameter and 20 mm thickness, what is the calculated tangential stress?
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Given that the longitudinal stress is defined as $σ_L = rac{pD}{4t}$, what is the longitudinal stress for an internal pressure of 4.5 MN/m² in a vessel with a diameter of 400 mm and wall thickness of 20 mm?
Given that the longitudinal stress is defined as $σ_L = rac{pD}{4t}$, what is the longitudinal stress for an internal pressure of 4.5 MN/m² in a vessel with a diameter of 400 mm and wall thickness of 20 mm?
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If the allowable stress in the steel is limited to 120 MN/m², what is the maximum internal pressure that can be applied to the 400 mm diameter vessel with 20 mm thickness?
If the allowable stress in the steel is limited to 120 MN/m², what is the maximum internal pressure that can be applied to the 400 mm diameter vessel with 20 mm thickness?
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What is the type of fracture expected to occur if the internal pressure in the vessel is increased until it bursts, given that tangential stress governs?
What is the type of fracture expected to occur if the internal pressure in the vessel is increased until it bursts, given that tangential stress governs?
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In a spherical tank with a wall thickness of 5/16 inch and a diameter of 4 ft, if the stress is limited to 8000 psi, what should you calculate?
In a spherical tank with a wall thickness of 5/16 inch and a diameter of 4 ft, if the stress is limited to 8000 psi, what should you calculate?
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If a water tank is 22 ft in diameter and made from 1/2 inch thick steel plates, what is the maximum height to which it can be filled if the circumferential stress is limited to 6000 psi?
If a water tank is 22 ft in diameter and made from 1/2 inch thick steel plates, what is the maximum height to which it can be filled if the circumferential stress is limited to 6000 psi?
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What factor primarily influences whether a vessel bursts under pressure?
What factor primarily influences whether a vessel bursts under pressure?
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Study Notes
Fundamental Concepts of Stress
- Stress is a measure of the material's response to external forces.
- Stress is simply the ratio of the external force to the cross-sectional area.
- Stress is measured in units of force per unit area (e.g., Pascals (Pa), pounds per square inch (psi)).
Types of Stress
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Normal Stress is stress developed when the force applied is perpendicular to the surface.
- Compressive Stress: The stress developed due to a compressive force that tends to shrink or shorten the member.
- Tensile Stress: The stress developed due to a tensile force that tends to elongate the member.
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Shear Stress is created by forces acting parallel to the surface.
- Shear stress arises when one section of the body slides past an adjacent section.
- Bearing Stress is the contact pressure between two surfaces of bodies.
Shear and Punching
- Shear stress can be categorized as:
- Single Shear: The force is acting on one plane.
- Double Shear: The force is distributed across two planes.
- Punching Shear is a specific case of shear stress where a hole is being punched through material.
Thin-walled Cylinders
- Thin-walled cylinders, such as tanks and pipes, are subjected to tensile stresses caused by pressure.
- Tangential Stress (Circumferential Stress), σt, is the stress developed in a longitudinal section resisting the bursting pressure.
- Longitudinal Stress, σL, is the stress developed in a transverse section also resisting the bursting pressure.
Calculation of Stresses in Cylinders
- Tangential Stress: σt = pD / 2t, where p is internal pressure, D is internal diameter, and t is wall thickness.
- Longitudinal Stress: σL = pD / 4t, where p is internal pressure, D is internal diameter, and t is wall thickness.
- Note: σt = 2σL - Tangential stress is twice the longitudinal stress.
Problem Example
- A cylindrical steel pressure vessel 400 mm in diameter with a wall thickness of 20 mm is subjected to an internal pressure of 4.5 MN/m2.
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Calculate the tangential and longitudinal stresses in the steel:
- Tangential Stress: σt = 45 MPa
- Longitudinal Stress: σl = 22.5 MPa
- If the internal pressure is increased until the vessel bursts, the fracture would occur along a longitudinal section (following the direction of the tangential stress) creating a "hoop" fracture.
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Description
Explore the essential principles of stress in materials and how it pertains to external forces. This quiz covers types of stress, including normal, shear, and bearing stress, along with their effects on material response. Test your understanding of these fundamental concepts in material science.
