Moment at Abutments of Arch Dam Calculator

Moment Formula:

\[ M_t = r \times ((p \times r) - F) \times \left(\frac{\sin(A)}{A} - \cos(A)\right) \]

Radius to Center Line (r):

Normal Radial Pressure (p):

N/m²

Thrust of Abutments (F):

Angle (A):

Tolerance:

Moment (Mt):

Definition: This calculator computes the moment acting on an arch dam at its abutments based on the dam's geometry and applied forces.

Purpose: It helps civil engineers determine the bending moment at dam abutments for structural analysis and design.

The calculator uses the formula:

\[ M_t = r \times ((p \times r) - F) \times \left(\frac{\sin(A)}{A} - \cos(A)\right) \]

Where:

Explanation: The formula calculates the bending moment considering the arch geometry, water pressure, and abutment reactions.

Details: Accurate moment calculation ensures structural stability, prevents overstressing, and helps optimize dam design for safety and economy.

Tips: Enter the radius, pressure, thrust, angle (in degrees), and tolerance percentage. All values except tolerance must be > 0.

Q1: What is normal radial pressure?
A: It's the water pressure acting perpendicular to the dam surface at the center line.

Q2: How is thrust at abutments determined?
A: It's calculated from the horizontal component of water pressure and arch geometry.

Q3: Why include a tolerance percentage?
A: Engineering calculations often include safety margins; ±5% is typical for preliminary designs.

Q4: What angle should be used?
A: Use the angle between the crown (top center) and the abutment radii.

Q5: How to interpret the results?
A: Compare the calculated moment with the dam's moment capacity to check structural adequacy.