Math Problem Statement

Determine the loads acting on the floor beam BE and the girder AC of the framing system.

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:

  1. 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.

  2. 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: qAC=9.96kPa×8m=79.68kN/mq_{AC} = 9.96 \, \text{kPa} \times 8 \, \text{m} = 79.68 \, \text{kN/m}
    • This represents the total distributed load on girder AC.
  3. 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: qBE=9.96kPa×4m=39.84kN/mq_{BE} = 9.96 \, \text{kPa} \times 4 \, \text{m} = 39.84 \, \text{kN/m}
    • This represents the total load that floor beam BE supports.
  4. 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:

  1. How do we calculate the reaction forces at points A, C, D, and F due to the distributed loads?
  2. What would be the bending moment in girder AC due to the distributed load?
  3. How do we compute shear forces in the floor beam BE and girder AC?
  4. Can the load on each beam be split further if we take into account the load distribution across individual members?
  5. 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