Continuous Beam Analysis Tool in Excel

Continuous Beam Analysis in Excel

This section provides guidance on creating an Excel tool for analyzing shear forces and bending moments in continuous beams. The formulas and functions needed are outlined below.

Key Elements of Continuous Beam Analysis

1. Beam Specifications:

   • Length of each beam segment.
   • Point loads and uniformly distributed loads (UDL).
   • Support locations (fixed, pinned).

2. Calculating Shear Force and Bending Moment:

   • The analysis involves segmenting the beam and calculating forces and moments at respective points.

Excel Setup

1. Input Data:

   • Create columns for:
     • Location (point A, point B, etc.)
     • Loads (Point load, UDL)
     • Length of segments

2. Output Data:

   • Create columns for:
     • Shear Force
     • Bending Moment

Formulas

1. Calculating Reactions at Supports

Use the following formula to calculate the reaction forces at the supports (assuming vertical loads):

• R_A = (Sum of moments about point A) / (Distance to support B)

If the support reactions need to be calculated based on multiple loads:

• For Point Loads:

  R_A = (Load_point1 * Distance_point1 + Load_point2 * Distance_point2) / Total_Span

• For Uniformly Distributed Load (UDL):

  For UDL over span:

  • R_A = Total_UDL * (Span / 2)

2. Shear Force Calculation

For shear force at a particular section (for example, after Point Load 1):

• At a Location "x":

If a point load is applied right before "x":

• V_x = R_A - (Point1_Load)

If there is a UDL along the preceding span "L":

• V_x = R_A - (Point1_Load + (UDL * Length_to_x))

3. Bending Moment Calculation

For bending moment calculation at a section:

• At a Location "x":

If there is no UDL in the left span:

• M_x = R_A * x - (Sum of moments due to loads up to x)

If there is a UDL:

• M_x = R_A * x - (Point_Load Distance_from_A) - (0.5 * UDL * Length_to_x^2)

Practical Example

Setup Data in Excel:

1. Input Data: (in columns A-D)

   • A: Location (A1, A2)
   • B: Point Load (e.g., 10, 5)
   • C: UDL (e.g., 2 across span)
   • D: Length of Span

2. Calculate Reactions: (in E1)

   • Input:
     • =B1 + B2 + (C1 * D1) (sum loads for reaction)

3. Shear Force: (in F1)

   • Input:
     • =E1 - B1 (for section right after point A)

4. Bending Moment: (in G1)

   • Input:
     • =E1*D1 - B1*(D1 - L) (where L is distance from reaction to point load)

Conclusion

This Excel framework simplifies continuous beam analysis by using structured data inputs and formulas to analyze shear forces and bending moments. It is essential to ensure that the calculations take into account the configuration of loads and spans accurately.

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