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Engineering
Civil Engineering
16-foot-long

16-foot-long

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A 16-foot-long single overhang beam is loaded as shown. Assuming a W8 x 35 determine the maximum bending stress developed. The informally distributed load of 3 k/ft include the weight of the beam. Given: A992 steel Fb = 30 ksi.
For W8 x 35 section properties see Table A3 (Textbook Appendix) (Provided)

**Wide Flange Shapes** ### Theoretical Dimensions and Properties for Designing #### Section Labels: - **W10 x 112** - **W8 x 67**, etc. #### Columns: 1. **Section Number**: Identifier for the specific wide flange shape 2. **Weight per Foot (lb.)**: Weight of the section per linear foot 3. **Area of Section (in.²)**: Cross-sectional area 4. **Depth of Section (in.)**: Overall depth 5. **Flange Width (bf)**: Width of the flange 6. **Flange Thickness (tf)**: Thickness of the flange 7. **Web Thickness (tw)**: Thickness of the web 8. **Moment of Inertia about X-X Axis (Ix)**: Resistance to bending 9. **Section Modulus about X-X Axis (Sx)**: Strength characteristic 10. **Radius of Gyration about X-X Axis (rx)** 11. **Moment of Inertia about Y-Y Axis (Iy)** 12. **Section Modulus about Y-Y Axis (Sy)** 13. **Radius of Gyration about Y-Y Axis (ry)** #### Diagram: - The diagram depicts a cross-sectional view of a wide flange shape. - Labeled with dimensions: - **d**: Depth - **bf**: Flange width - **tf** and **tw**: Flange and web thicknesses ### Sample Data (Partial View): - **W10 x 112**: - Weight: 32.9 lb/ft - Area: 11.36 in.² - Depth: 10.415 in. - Flange Width: 15.250 in. - Flange Thickness: 0.755 in. - Web Thickness: 0.715 in. - Ix: 716 in.⁴ - Sx: 126 in.³ - Iy: 45.3 in.⁴ - Sy: 6.82 in.³ The table provides comprehensive data for engineers to select appropriate wide flange shapes based on required structural properties. All shapes have parallel-faced flanges.
Transcribed Image Text:**Wide Flange Shapes** ### Theoretical Dimensions and Properties for Designing #### Section Labels: - **W10 x 112** - **W8 x 67**, etc. #### Columns: 1. **Section Number**: Identifier for the specific wide flange shape 2. **Weight per Foot (lb.)**: Weight of the section per linear foot 3. **Area of Section (in.²)**: Cross-sectional area 4. **Depth of Section (in.)**: Overall depth 5. **Flange Width (bf)**: Width of the flange 6. **Flange Thickness (tf)**: Thickness of the flange 7. **Web Thickness (tw)**: Thickness of the web 8. **Moment of Inertia about X-X Axis (Ix)**: Resistance to bending 9. **Section Modulus about X-X Axis (Sx)**: Strength characteristic 10. **Radius of Gyration about X-X Axis (rx)** 11. **Moment of Inertia about Y-Y Axis (Iy)** 12. **Section Modulus about Y-Y Axis (Sy)** 13. **Radius of Gyration about Y-Y Axis (ry)** #### Diagram: - The diagram depicts a cross-sectional view of a wide flange shape. - Labeled with dimensions: - **d**: Depth - **bf**: Flange width - **tf** and **tw**: Flange and web thicknesses ### Sample Data (Partial View): - **W10 x 112**: - Weight: 32.9 lb/ft - Area: 11.36 in.² - Depth: 10.415 in. - Flange Width: 15.250 in. - Flange Thickness: 0.755 in. - Web Thickness: 0.715 in. - Ix: 716 in.⁴ - Sx: 126 in.³ - Iy: 45.3 in.⁴ - Sy: 6.82 in.³ The table provides comprehensive data for engineers to select appropriate wide flange shapes based on required structural properties. All shapes have parallel-faced flanges.
### Structural Analysis of a W8x35 Beam #### Beam Cross-Section and Dimensions The image on the left displays a diagram of a W8x35 I-beam cross-section with the following dimensions: - **Flange Width (\(b_f\))**: 8.02 inches - **Flange Thickness (\(t_f\))**: 0.495 inches - **Web Thickness (\(t_w\))**: 0.310 inches - **Depth (\(d\))**: 8.12 inches Additional properties of the beam include: - **Moment of Inertia (\(I_x\))**: 127 in\(^4\) - **Section Modulus (\(S_x\))**: 31.2 in\(^3\) - **Depth (\(d\))**: 8.12 inches - **Distance to the Center (\(c\))**: 4.06 inches #### Beam and Load Diagram The upper right section of the image illustrates a simply supported beam subjected to two types of loads: - A **concentrated load (P = 6k)** applied at a point 4 feet from support A. - A **uniformly distributed load (w = 3k/ft)** over an 8-foot section between points B and C. The supports are located at points A and C. #### Shear Force (\(V\)) and Bending Moment (\(M\)) Diagrams The diagram on the bottom right provides the shear force and bending moment diagrams for the beam: - **Shear Force (\(V\)) Diagram**: - Begins at +36 kips at A. - Changes linearly, crossing zero at the point of load application. - Maximum positive shear of +24 kips and negative shear of -24 kips are observed. - **Bending Moment (\(M\)) Diagram**: - The moment starts at zero at both supports A and C. - Maximum positive moment is 54 kip-ft, occurring between A and B. - The moment becomes negative under the distributed load reaching a maximum negative value of -24 kip-ft. This detailed analysis is essential for understanding stress distribution and designing structurally sound beams in engineering applications.
Transcribed Image Text:### Structural Analysis of a W8x35 Beam #### Beam Cross-Section and Dimensions The image on the left displays a diagram of a W8x35 I-beam cross-section with the following dimensions: - **Flange Width (\(b_f\))**: 8.02 inches - **Flange Thickness (\(t_f\))**: 0.495 inches - **Web Thickness (\(t_w\))**: 0.310 inches - **Depth (\(d\))**: 8.12 inches Additional properties of the beam include: - **Moment of Inertia (\(I_x\))**: 127 in\(^4\) - **Section Modulus (\(S_x\))**: 31.2 in\(^3\) - **Depth (\(d\))**: 8.12 inches - **Distance to the Center (\(c\))**: 4.06 inches #### Beam and Load Diagram The upper right section of the image illustrates a simply supported beam subjected to two types of loads: - A **concentrated load (P = 6k)** applied at a point 4 feet from support A. - A **uniformly distributed load (w = 3k/ft)** over an 8-foot section between points B and C. The supports are located at points A and C. #### Shear Force (\(V\)) and Bending Moment (\(M\)) Diagrams The diagram on the bottom right provides the shear force and bending moment diagrams for the beam: - **Shear Force (\(V\)) Diagram**: - Begins at +36 kips at A. - Changes linearly, crossing zero at the point of load application. - Maximum positive shear of +24 kips and negative shear of -24 kips are observed. - **Bending Moment (\(M\)) Diagram**: - The moment starts at zero at both supports A and C. - Maximum positive moment is 54 kip-ft, occurring between A and B. - The moment becomes negative under the distributed load reaching a maximum negative value of -24 kip-ft. This detailed analysis is essential for understanding stress distribution and designing structurally sound beams in engineering applications.
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