### Analysis of a Flanged Wooden Beam**Problem Statement:**A flanged wooden shape is used to support the loads shown. The dimensions of the shape are shown in the diagram. Consider the entire 16 ft length of the beam and determine:(a) Calculate the inertia.(b) Sketch the shear and moment diagram for this beam.(c) Determine the maximum tensile bending stress in the beam. Sketch the bending stress distribution at this section and show detailed calculations.(d) Determine the maximum compressive bending stress in the beam. Sketch the bending stress distribution at this section and show detailed calculations.(e) Determine the maximum shear stress in the beam. Sketch the shear stress distribution and show the calculations.---**Load and Beam Configuration:**- An evenly distributed load of 1 kip/ft is applied over a 6 ft section from point A.- A point load of 2 kips is applied at point C, which is 9 ft from A.- Another point load of 2.2 kips is applied at point E, which is 16 ft from A.**Support Setup:**- A pinned support is located at point A.- A roller support is located at point D, 12 ft from point A.---**Cross-Section Dimensions:**The cross-section of the beam is shown on the right with the following dimensions:1. **Top flange:** - Width: 8 inches - Thickness: 1 inch2. **Web:** - Height: 10 inches - Thickness: 1 inch3. **Bottom flange:** - Width: 8 inches - Thickness: 1 inch4. **Overall depth of the cross-section:** - 12 inches**Neutral Axis:**- Located 7 inches from the top of the beam.**Designate axes:**- y-axis runs vertically through the center of the web.- z-axis runs horizontally through the neutral axis.**Note:** Diagrams of bending stress and shear stress distributions, as well as calculated results for each section, should be provided to fully address each part of the problem statement.

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A flanged wooden shape is used to support the loads shown. The dimensions of the shape are shown. Consider the entire 16 ft length of the beam, and determine (a) Calculate the inertia (b) Sketch the shear and moment diagram for this beam (c) the maximum tensile bending stress in the beam (sketch the bending stress distribution at this section and show detailed calculations) (d) the maximum compressive bending stress in the beam (sketch the bending stress distribution at this section and show detailed calculations)) (e) the maximum shear stress in the beam and (sketch the shear stress distribution and show the calculations) 4 in. 1 in. 2 kips 2.2 kips (1) 1 in. 1 kip/ft 7 in. 12 in. (2) 10 in. 5 in. (3) B C D E 8 in. 3 ft * 3ft 4 ft - 1 in. 6 ft

A flanged wooden shape is used to support the loads shown. The dimensions of the shape are shown. Consider the entire 16 ft length of the beam, and determine (a) Calculate the inertia (b) Sketch the shear and moment diagram for this beam (c) the maximum tensile bending stress in the beam (sketch the bending stress distribution at this section and show detailed calculations) (d) the maximum compressive bending stress in the beam (sketch the bending stress distribution at this section and show detailed calculations)) (e) the maximum shear stress in the beam and (sketch the shear stress distribution and show the calculations) 4 in. 1 in. 2 kips 2.2 kips (1) 1 in. 1 kip/ft 7 in. 12 in. (2) 10 in. 5 in. (3) B C D E 8 in. 3 ft * 3ft 4 ft - 1 in. 6 ft

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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Question

### Analysis of a Flanged Wooden Beam

**Problem Statement:**

A flanged wooden shape is used to support the loads shown. The dimensions of the shape are shown in the diagram. Consider the entire 16 ft length of the beam and determine:

(a) Calculate the inertia.

(b) Sketch the shear and moment diagram for this beam.

(c) Determine the maximum tensile bending stress in the beam. Sketch the bending stress distribution at this section and show detailed calculations.

(d) Determine the maximum compressive bending stress in the beam. Sketch the bending stress distribution at this section and show detailed calculations.

(e) Determine the maximum shear stress in the beam. Sketch the shear stress distribution and show the calculations.

---

**Load and Beam Configuration:**

- An evenly distributed load of 1 kip/ft is applied over a 6 ft section from point A.
- A point load of 2 kips is applied at point C, which is 9 ft from A.
- Another point load of 2.2 kips is applied at point E, which is 16 ft from A.

**Support Setup:**

- A pinned support is located at point A.
- A roller support is located at point D, 12 ft from point A.

---

**Cross-Section Dimensions:**

The cross-section of the beam is shown on the right with the following dimensions:

1. **Top flange:**
- Width: 8 inches
- Thickness: 1 inch

2. **Web:**
- Height: 10 inches
- Thickness: 1 inch

3. **Bottom flange:**
- Width: 8 inches
- Thickness: 1 inch

4. **Overall depth of the cross-section:**
- 12 inches

**Neutral Axis:**
- Located 7 inches from the top of the beam.

**Designate axes:**
- y-axis runs vertically through the center of the web.
- z-axis runs horizontally through the neutral axis.

**Note:** Diagrams of bending stress and shear stress distributions, as well as calculated results for each section, should be provided to fully address each part of the problem statement.

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