A steel frame office building has the framework section shown in the diagram. The vertical supports are 2.2 m apart and 52.8 m high. If the diagonal braces have a length of 2.75 m,... A steel frame office building has the framework section shown in the diagram. The vertical supports are 2.2 m apart and 52.8 m high. If the diagonal braces have a length of 2.75 m, how many are needed for this section?
Understand the Problem
The question describes a steel frame office building with vertical supports and diagonal braces. Given the height of the building section (52.8 m) and the length of the diagonal braces (2.75 m), we need to determine the number of diagonal braces required for that section. We must estimate the number of stories based on the image and the height/width ratio, and then multiply by the number of supports per story.
Answer
The total number of diagonal braces needed is $46$.
Answer for screen readers
The total number of diagonal braces needed for the section is $46$.
Steps to Solve
- Determine the number of vertical sections Calculate the total height divided by the distance between the vertical supports to find how many vertical sections are present.
Given:
- Height of the building section = 52.8 m
- Distance between vertical supports = 2.2 m
Calculating: $$ \text{Number of vertical supports} = \frac{52.8 \text{ m}}{2.2 \text{ m}} \approx 24 $$
- Identify the number of diagonal braces per section Every vertical section typically has one diagonal brace connecting to two vertical supports.
If there are 24 vertical supports, there would be ( 24 - 1 = 23 ) sections formed.
- Calculate the total number of diagonal braces For each section, there are two diagonal braces (one for each direction: left and right). Therefore, multiply the number of sections by 2.
Calculating: $$ \text{Total diagonal braces} = 23 \times 2 = 46 $$
The total number of diagonal braces needed for the section is $46$.
More Information
In steel frame construction, diagonal braces provide essential structural stability by transferring loads and resisting lateral forces. Each brace supports the framework significantly, ensuring safety and durability.
Tips
- Miscalculating the number of vertical supports by not considering the correct height or distance between them.
- Forgetting to account for two diagonal braces per section, which can lead to underestimating the total.
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