Assume that, due to a construction error, the beam of the previous two examples was placed incorrectly in the field and the small dimension (7 ½ in. dressed) was oriented vertically. For the same span length and loading, calculate the maximum bending stress that would be developed.
Assume that, due to a construction error, the beam of the previous two examples was placed incorrectly in the field and the small dimension (7 ½ in. dressed) was oriented vertically. For the same span length and loading, calculate the maximum bending stress that would be developed.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Assume that, due to a construction error, the beam of the previous two examples was placed incorrectly in the field and the small dimension (7 ½ in. dressed) was oriented vertically. For the same span length and loading, calculate the maximum bending stress that would be developed.
Example 1: A beam with a cross section of 6 in. x 12 in. is subjected to a bending moment M of 24 kip.ft.
Example 2: The timber member of Example 1 is used as a simply supported beam on a 16-ft span carrying a uniformly distributed line load of 400 lb/ft as shown below.
Transcribed Image Text:### Structural Beam Analysis
#### Diagram Explanation:
**Left Diagram:**
This is a schematic of a simply supported beam subjected to a uniform distributed load.
- The beam has a length of 16 feet.
- It is subjected to a uniform distributed load of 400 pounds per foot (lb/ft).
- The supports at each end of the beam indicate that it is simply supported.
**Right Diagram:**
This diagram illustrates the cross-sectional properties of the beam.
- The cross-section is rectangular with a height (**h**) of 11.5 inches and a base (**b**) of 7.5 inches.
- The diagram includes the **centroidal axis and neutral axis**, labeled as "XX", which runs horizontally through the center of the cross-section.
- Concentric curves are illustrated to indicate stress distribution across the section.
These diagrams are essential for understanding the bending behavior and stress distribution in the beam under the given load. The calculations derived from such diagrams help inform design decisions and ensure structural integrity.
Transcribed Image Text:**Transcription of Diagram for Educational Content**
This diagram illustrates a rectangular section with defined dimensions and structural details, commonly used in engineering and architectural contexts.
- **Dimensions of the Rectangle:**
- The base width of the rectangle is labeled as \( b = 11.5 \) inches.
- The height of the rectangle is indicated as \( h = 7.5 \) inches.
- **Structural Details:**
- The rectangle features a horizontal line labeled as the "Centroidal axis and neutral axis," marked with "X X" across the section. This axis is central to the structure's balance and is significant in understanding how forces and moments act upon the body when subjected to loading.
- **Additional Features:**
- A series of curved lines are shown within the rectangle, likely representing stress distribution or bending within the section under certain loading conditions. These curves suggest how the material might flex or react when a force is applied.
This diagram could serve to help visualize concepts related to moments of inertia, bending stress, or other mechanical properties in structural analysis.
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