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Why when plugging the formula for crossectional it gives a different value than 6650m2. The table shown, shows 6650 mm2 and with the equation for A= is 6617 please solve and make sure with the equation

Why when plugging the formula for crossectional it gives a different value than 6650m2. The table shown, shows 6650 mm2 and with the equation for A= is 6617 please solve and make sure with the equation

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Why when plugging the formula for crossectional it gives a different value than 6650m2. The table shown, shows 6650 mm2 and with the equation for A= is 6617 please solve and make sure with the equation it gives you 6650mm2
**Appendix E: Properties of Rolled-Steel Shapes** **W Shapes (Wide-Flange Shapes) (SI Units)** The table contains detailed specifications for a variety of wide-flange steel shapes, identified by their designation, area, and various dimensions. Each entry provides the following information: 1. **Designation**: Identifies the shape using the letter 'W' followed by the nominal depth in millimeters and the mass in kilograms per meter. 2. **Area (A, mm²)**: The cross-sectional area of the shape. 3. **Depth (d, mm)**: The depth of the steel shape. 4. **Flange Specifications**: - **Width (b, mm)**: The width of the flange. - **Thickness (t₁, mm)**: The thickness of the flange. 5. **Web Specifications**: - **Thickness (tᵥ, mm)**: The thickness of the web. 6. **Axis X-X**: - **lₓ (10⁶ mm⁴)**: Moment of inertia about the X-X axis. - **Sₓ (10³ mm³)**: Section modulus about the X-X axis. - **rₓ (mm)**: Radius of gyration about the X-X axis. 7. **Axis Y-Y**: - **lᵧ (10⁶ mm⁴)**: Moment of inertia about the Y-Y axis. - **Sᵧ (10³ mm³)**: Section modulus about the Y-Y axis. - **rᵧ (mm)**: Radius of gyration about the Y-Y axis. **Highlighted Sections**: Certain entries are highlighted with a red background to draw attention. For example, the W360 × 51 and W310 × 143 sections are highlighted, possibly indicating preferred or standard sizes. **Diagram**: A diagram at the top-right illustrates the dimensions of the W shape with labeled axes (X, Y) and thicknesses (t₁, tᵥ). **Note**: A footnote explains the designation convention: "A wide-flange shape is designated by the letter W followed by the nominal depth in millimeters and the mass in kilograms per meter."
Transcribed Image Text:**Appendix E: Properties of Rolled-Steel Shapes** **W Shapes (Wide-Flange Shapes) (SI Units)** The table contains detailed specifications for a variety of wide-flange steel shapes, identified by their designation, area, and various dimensions. Each entry provides the following information: 1. **Designation**: Identifies the shape using the letter 'W' followed by the nominal depth in millimeters and the mass in kilograms per meter. 2. **Area (A, mm²)**: The cross-sectional area of the shape. 3. **Depth (d, mm)**: The depth of the steel shape. 4. **Flange Specifications**: - **Width (b, mm)**: The width of the flange. - **Thickness (t₁, mm)**: The thickness of the flange. 5. **Web Specifications**: - **Thickness (tᵥ, mm)**: The thickness of the web. 6. **Axis X-X**: - **lₓ (10⁶ mm⁴)**: Moment of inertia about the X-X axis. - **Sₓ (10³ mm³)**: Section modulus about the X-X axis. - **rₓ (mm)**: Radius of gyration about the X-X axis. 7. **Axis Y-Y**: - **lᵧ (10⁶ mm⁴)**: Moment of inertia about the Y-Y axis. - **Sᵧ (10³ mm³)**: Section modulus about the Y-Y axis. - **rᵧ (mm)**: Radius of gyration about the Y-Y axis. **Highlighted Sections**: Certain entries are highlighted with a red background to draw attention. For example, the W360 × 51 and W310 × 143 sections are highlighted, possibly indicating preferred or standard sizes. **Diagram**: A diagram at the top-right illustrates the dimensions of the W shape with labeled axes (X, Y) and thicknesses (t₁, tᵥ). **Note**: A footnote explains the designation convention: "A wide-flange shape is designated by the letter W followed by the nominal depth in millimeters and the mass in kilograms per meter."
The image appears to be an educational document outlining steps to calculate the area of a cross-section for a structural component. Below is a detailed transcription and explanation for each step. --- ### Step 1 **a) Diagram and Given Data** A diagram of the cross-section is displayed with the following labeled dimensions: - **d** = 317 mm - **tw** = 7.6 mm (thickness of the web) - **bf** = 167 mm (width of the flange) - **tf** = 13.2 mm (thickness of the flange) The diagram illustrates a typical I-beam cross-section with these dimensions labeled accordingly. --- ### Step 2 **b) Calculation of the Area** The area of the given cross-section is calculated as follows: 1. **Formula for Area Calculation:** \[ \text{Area(A)} = (d \times b_f) - (d - 2t_f) \times (b_f - t_w) \] 2. **Substitution of Values:** \[ \text{Area} = (317 \times 167) - (317 - 2 \times 13.2) \times (167 - 7.6) \] \[ \text{Area} = 6617.36 \, \text{mm}^2 \] 3. **Alternative Method:** \[ \text{Area} = 2 \, b_f \, t_f + t_w \, (d - 2t_f) \] \[ \text{Area} = 2 \times (167 \times 13.2) + 7.6 \times (317 - 2 \times 13.2) \] \[ \text{Area} = 6617.36 \, \text{mm}^2 \] Hence, for the given cross-section, the area comes out to be: \[ A = 6617.36 \, \text{mm}^2 \] These calculations ensure that both methods yield the same cross-sectional area, confirming the accuracy of the process.
Transcribed Image Text:The image appears to be an educational document outlining steps to calculate the area of a cross-section for a structural component. Below is a detailed transcription and explanation for each step. --- ### Step 1 **a) Diagram and Given Data** A diagram of the cross-section is displayed with the following labeled dimensions: - **d** = 317 mm - **tw** = 7.6 mm (thickness of the web) - **bf** = 167 mm (width of the flange) - **tf** = 13.2 mm (thickness of the flange) The diagram illustrates a typical I-beam cross-section with these dimensions labeled accordingly. --- ### Step 2 **b) Calculation of the Area** The area of the given cross-section is calculated as follows: 1. **Formula for Area Calculation:** \[ \text{Area(A)} = (d \times b_f) - (d - 2t_f) \times (b_f - t_w) \] 2. **Substitution of Values:** \[ \text{Area} = (317 \times 167) - (317 - 2 \times 13.2) \times (167 - 7.6) \] \[ \text{Area} = 6617.36 \, \text{mm}^2 \] 3. **Alternative Method:** \[ \text{Area} = 2 \, b_f \, t_f + t_w \, (d - 2t_f) \] \[ \text{Area} = 2 \times (167 \times 13.2) + 7.6 \times (317 - 2 \times 13.2) \] \[ \text{Area} = 6617.36 \, \text{mm}^2 \] Hence, for the given cross-section, the area comes out to be: \[ A = 6617.36 \, \text{mm}^2 \] These calculations ensure that both methods yield the same cross-sectional area, confirming the accuracy of the process.
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