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Questions and Answers
What does tensile stress describe?
What does tensile stress describe?
- Intensity of force acting tangent to an area.
- The point where the ratio P/A is at its minimum.
- Normal force that 'pulls' or 'stretches' the area element. (correct)
- Normal force that 'pushes' or 'compresses' the area element.
Shear stress is the intensity of force acting normal to an area.
Shear stress is the intensity of force acting normal to an area.
False (B)
What is the primary focus of mechanics of materials?
What is the primary focus of mechanics of materials?
- The external loads applied to a body.
- The internal loads and deformations within a body due to external loads. (correct)
- The aesthetic design of structures.
- The cost of materials used in construction.
What is the symbol used to represent shear stress?
What is the symbol used to represent shear stress?
Stress is defined as the area per unit force acting on that area.
Stress is defined as the area per unit force acting on that area.
In SI units, force is expressed in newtons (N) and area in square meters (m2). A N/m2 is a(n) _______
In SI units, force is expressed in newtons (N) and area in square meters (m2). A N/m2 is a(n) _______
What are the two fundamental requirements for the equilibrium of a rigid body?
What are the two fundamental requirements for the equilibrium of a rigid body?
Match the following terms with their descriptions:
Match the following terms with their descriptions:
Which assumption is made when analyzing average normal stress in an axially loaded bar?
Which assumption is made when analyzing average normal stress in an axially loaded bar?
A ______ is a diagram used to calculate the forces acting on a body.
A ______ is a diagram used to calculate the forces acting on a body.
Which of the following is NOT a type of internal resultant loading?
Which of the following is NOT a type of internal resultant loading?
Normal stresses are considered negative for tensile stresses and positive for compressive stresses.
Normal stresses are considered negative for tensile stresses and positive for compressive stresses.
The objective of a free-body diagram (FBD) is to determine the external forces acting on a body.
The objective of a free-body diagram (FBD) is to determine the external forces acting on a body.
To find the maximum average normal stress in a bar with varying cross-sectional area and external loads, what ratio needs to be maximized?
To find the maximum average normal stress in a bar with varying cross-sectional area and external loads, what ratio needs to be maximized?
Match the following internal resultant loadings with their description:
Match the following internal resultant loadings with their description:
What is the formula for calculating average stress?
What is the formula for calculating average stress?
What is the sign convention for axial force P when it causes compression in a member?
What is the sign convention for axial force P when it causes compression in a member?
Average normal stress is calculated by multiplying the internal resultant force P by the cross-sectional area A ($σ = P * A$).
Average normal stress is calculated by multiplying the internal resultant force P by the cross-sectional area A ($σ = P * A$).
When determining internal loading in an axially loaded member, at what point should the member be sectioned relative to its longitudinal axis?
When determining internal loading in an axially loaded member, at what point should the member be sectioned relative to its longitudinal axis?
The shear stress component acts in the ______ of the sectioned area.
The shear stress component acts in the ______ of the sectioned area.
In the context of shear stress, what does 'V' represent?
In the context of shear stress, what does 'V' represent?
Simple or direct shear is caused by an indirect action of an applied load.
Simple or direct shear is caused by an indirect action of an applied load.
For a double shear connection, how is the shear force 'V' related to the applied force 'F'?
For a double shear connection, how is the shear force 'V' related to the applied force 'F'?
Match the type of shear with its description:
Match the type of shear with its description:
What is the primary consideration when designing structural elements or mechanical components?
What is the primary consideration when designing structural elements or mechanical components?
A Factor of Safety (F.S.) less than 1 is acceptable to avoid potential failure of a member.
A Factor of Safety (F.S.) less than 1 is acceptable to avoid potential failure of a member.
What two steps are essential when using average normal stress and shear stress equations for analysis?
What two steps are essential when using average normal stress and shear stress equations for analysis?
The average shear stress ($\tau_{avg}$) is calculated using the formula $\tau_{avg} = V/______$, where V is the internal shear force.
The average shear stress ($\tau_{avg}$) is calculated using the formula $\tau_{avg} = V/______$, where V is the internal shear force.
Match the following steps with their corresponding descriptions when solving for average shear stress.
Match the following steps with their corresponding descriptions when solving for average shear stress.
In the context of designing simple connections, what does the following formula represent? $A = \frac{P}{\sigma_{allow}}$
In the context of designing simple connections, what does the following formula represent? $A = \frac{P}{\sigma_{allow}}$
When designing a simple connection, the cross-sectional area is not a key parameter.
When designing a simple connection, the cross-sectional area is not a key parameter.
What condition must be met regarding the force acting on a tension member?
What condition must be met regarding the force acting on a tension member?
Flashcards
Stress
Stress
The intensity of the internal force acting on a material per unit area.
Normal Stress (σ)
Normal Stress (σ)
Force per unit area acting perpendicular to a surface.
Tensile Stress
Tensile Stress
Normal stress that results from a pulling force, causing elongation.
Compressive Stress
Compressive Stress
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Shear Stress (Ï„)
Shear Stress (Ï„)
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Axially Loaded Bar
Axially Loaded Bar
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Average Normal Stress (σ = P/A)
Average Normal Stress (σ = P/A)
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Maximum Average Normal Stress
Maximum Average Normal Stress
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Free-body diagram
Free-body diagram
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Equation of equilibrium (EoE)
Equation of equilibrium (EoE)
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Average shear stress
Average shear stress
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Cross-sectional area (A)
Cross-sectional area (A)
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Average normal stress (σ)
Average normal stress (σ)
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Factor of Safety (F.S)
Factor of Safety (F.S)
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Allowable stress
Allowable stress
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Design of simple connections
Design of simple connections
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Sign Convention for Force P
Sign Convention for Force P
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Average Normal Stress
Average Normal Stress
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Single Shear
Single Shear
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Double Shear
Double Shear
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Multiple Shear
Multiple Shear
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Procedure for Shear Analysis
Procedure for Shear Analysis
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Equilibrium of a Deformable Body
Equilibrium of a Deformable Body
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Free-Body Diagram (FBD)
Free-Body Diagram (FBD)
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Normal Force (N)
Normal Force (N)
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Shear Force (V)
Shear Force (V)
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Torsional Moment (T)
Torsional Moment (T)
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Bending Moment (M)
Bending Moment (M)
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Study Notes
Introduction to Stress
- Mechanics of materials studies the relationship between external and internal loads on a body.
- It also examines the deformations and stability of a body under external forces.
- Stress is defined as force per unit area. The unit is Pascal (Pa) or N/m².
Equilibrium of a Deformable Body
- Equilibrium requires a balance of forces and moments.
- ΣF=0 (Sum of forces equals zero)
- ΣΜ=0 (Sum of moments equals zero)
- Calculates these forces using a free-body diagram (FBD).
Stress Types
- Normal force acts perpendicular to the area (push or pull).
- Shear force acts in the plane of the area (causes sliding).
- Torque (torsional moment) causes twisting.
- Bending moment causes bending.
Average Normal Stress
- Examples include structural members, truss members, hangers, and bolts.
- Assumes uniform deformation and that the force is applied along the centroidal axis of the cross-section.
Average Shear Stress
- Shear stress acts in the plane of a sectioned area.
- Consider forces acting on the bar and identify planes of failure.
- Free-body diagrams show shear forces to ensure equilibrium.
- Single shear: The force is applied across a single section.
- Double shear: The force is applied across two sections.
Allowable Stress
- Used in designing structures to prevent failure under operating conditions.
- Factor of safety (FS) = Failure load / Allowable load.
- The allowable load is less than the failure load of the member to ensure safety.
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