Tension Member A36 Steel Plate P Calculate Tension Capacity of line abcde (A„) 1. 2. abfcgde (A) 3. abfgde (A,), and 4. Yielding over A gross
Tension Member A36 Steel Plate P Calculate Tension Capacity of line abcde (A„) 1. 2. abfcgde (A) 3. abfgde (A,), and 4. Yielding over A gross
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![This diagram is a detailed illustration of a gusset plate connection to a tension member using bolts. The primary focus is calculating the tension capacity of various lines through the plate. Below is a description and explanation of the components and steps involved:
### Components
- **Gusset Plate**: A structural component to connect beams and columns, shown here with dimensions of 12 inches in height.
- **Bolts**: The diagram specifies "10 – 7/8” Bolts" used to secure the connection.
- **Plate Thickness**: Labeled as \( t = \frac{1}{2}" \).
- **Tension Member**: Specified as an "A36 Steel Plate", which is subject to axial tension force denoted as \( P_u \).
### Dimensions and Lines
- **Bolt Placement**: Bolts are placed in a staggered pattern, with horizontal distances of 3 inches between them and vertical spacing of 2 inches between each bolt.
- **Lines of Consideration for Tension Capacity**:
- **Line abcde (A_{n})**: A red dashed line following a staggered pattern around bolts.
- **Line abfcgde (A_{n'})**: A black dashed line diverging from line 1, with extra bolting points considered.
- **Line abfgde (A_{n''})**: Another staggered path considered for tension capacity.
- **Yielding Consideration**: Indicated as the evaluation of yielding over the \( A_{gross} \).
### Points and Areas
- **Points a, b, c, d, e, f, g**: Critical points on the plate where tension lines are considered.
- **Cross-sectional Areas**:
- \( A_n \) (net area) and \( A_g \) (gross area) are used to evaluate the tensile strength under different failure paths.
### Calculation Instructions
The tension capacity of the various lines through the plate is to be calculated as follows:
1. **Line abcde**: Analyze the net tensile area \( A_n \).
2. **Line abfcgde**: Consider additional bolt holes and evaluate \( A_{n'} \).
3. **Line abfgde**: Further evaluates net area with alternative bolt line \( A_{n''} \).
4. **Yielding**: Determine potential yielding using the gross sectional area \( A_{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F330ed3a3-f99b-4d8a-b363-50acb4ad2b33%2F24f59f5b-41ca-4639-92d6-dfdaf34c7c2e%2F6m8891q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This diagram is a detailed illustration of a gusset plate connection to a tension member using bolts. The primary focus is calculating the tension capacity of various lines through the plate. Below is a description and explanation of the components and steps involved:
### Components
- **Gusset Plate**: A structural component to connect beams and columns, shown here with dimensions of 12 inches in height.
- **Bolts**: The diagram specifies "10 – 7/8” Bolts" used to secure the connection.
- **Plate Thickness**: Labeled as \( t = \frac{1}{2}" \).
- **Tension Member**: Specified as an "A36 Steel Plate", which is subject to axial tension force denoted as \( P_u \).
### Dimensions and Lines
- **Bolt Placement**: Bolts are placed in a staggered pattern, with horizontal distances of 3 inches between them and vertical spacing of 2 inches between each bolt.
- **Lines of Consideration for Tension Capacity**:
- **Line abcde (A_{n})**: A red dashed line following a staggered pattern around bolts.
- **Line abfcgde (A_{n'})**: A black dashed line diverging from line 1, with extra bolting points considered.
- **Line abfgde (A_{n''})**: Another staggered path considered for tension capacity.
- **Yielding Consideration**: Indicated as the evaluation of yielding over the \( A_{gross} \).
### Points and Areas
- **Points a, b, c, d, e, f, g**: Critical points on the plate where tension lines are considered.
- **Cross-sectional Areas**:
- \( A_n \) (net area) and \( A_g \) (gross area) are used to evaluate the tensile strength under different failure paths.
### Calculation Instructions
The tension capacity of the various lines through the plate is to be calculated as follows:
1. **Line abcde**: Analyze the net tensile area \( A_n \).
2. **Line abfcgde**: Consider additional bolt holes and evaluate \( A_{n'} \).
3. **Line abfgde**: Further evaluates net area with alternative bolt line \( A_{n''} \).
4. **Yielding**: Determine potential yielding using the gross sectional area \( A_{
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