Math Problem Statement
Solution
The problem involves a roof subjected to a uniformly distributed load of 9.96 kPa. The framing system consists of a floor beam BE and a girder AC, and the goal is to determine the loads acting on these members. Here is how you can approach the problem:
Given Information:
- Uniformly distributed load (UDL): 9.96 kPa
- Dimensions:
- Spacing between beams: 4 m (2 beams), so the total width is 8 m
- Height of the column: 6 m
Step-by-step Breakdown:
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Area covered by load: The load is spread across the area of the roof that each beam supports. The distributed load is given in kPa (kN/m²), which means kilonewtons per square meter of surface area.
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Determine the load on the girder AC:
- The roof load is distributed across the width of the building (8 m), but each beam supports a portion of this load.
- Since the girder AC supports two beams (each spaced 4 m apart), the total load on the girder is:
- This represents the total distributed load on girder AC.
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Determine the load on the floor beam BE:
- Each floor beam supports the load from a portion of the roof spanning the width of the beam, which is 4 m.
- Therefore, the distributed load on each floor beam is:
- This represents the total load that floor beam BE supports.
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Conclusion:
- The distributed load acting on girder AC is 79.68 kN/m.
- The distributed load acting on floor beam BE is 39.84 kN/m.
Would you like more details on how to solve for the reactions at the supports or the internal forces in the beams?
Relative Questions:
- How do we calculate the reaction forces at points A, C, D, and F due to the distributed loads?
- What would be the bending moment in girder AC due to the distributed load?
- How do we compute shear forces in the floor beam BE and girder AC?
- Can the load on each beam be split further if we take into account the load distribution across individual members?
- How would different loading conditions (e.g., point loads) change the analysis?
Tip:
When working with uniformly distributed loads, always convert the load into a per-meter basis (kN/m) before calculating reactions and internal forces to simplify analysis.
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Math Problem Analysis
Mathematical Concepts
Structural Engineering
Load Distribution
Statics
Formulas
Load on girder AC = Uniformly distributed load (UDL) * Width covered by the girder
Load on floor beam BE = UDL * Width covered by the beam
Theorems
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Suitable Grade Level
University
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