St. Venant Torsional Constant

J.ts

/**
 * St. Venant torsional constant for structural engineering mathematics.
 *
 * @remarks Symbol: `J`.
 *
 * @example Taken from page I-57 the 2013 edition of the AISI Manual for Cold-Formed Steel Design - Vol 1.
 *     const J = new StVenantTorsionalConstant( 9.000, 2.500, 0.773, 0.059, 0.1875 );
 *     J.value = 0.00102;
 *
 * @version 1.0.0
 */

// This class needs on Lodash.js for its private `empty` method.
import _ from 'lodash';

/**
 * Begin `StVenantTorsionalConstant` class.
 * 
 * @since 1.0.0
 */
class StVenantTorsionalConstant {
  /**
   * Total outer height. Symbol: `A'`.
   * 
   * @since 1.0.0
   */
  public aPrime: number;

  /**
   * Total outer width. Symbol: `B'`.
   * 
   * @since 1.0.0
   */
  public bPrime: number;

  /**
   * Total height of lips (if applicable). Symbol: `C'`.
   * 
   * @since 1.0.0
   */
  public cPrime: number;

  /**
   * Shape thickness. Symbol: `t`.
   * 
   * @since 1.0.0
   */
  public t: number;

  /**
   * Half-thickness.
   * 
   * @since 1.0.0
   */
  public halfThickness: number;

  /**
   * Inner-bend radius. Symbol: `R`.
   * 
   * @since 1.0.0
   */
  public R: number;

  /**
   * For section with stiffener lips. Symbol: `α`.
   * 
   * @since 1.0.0
   */
  public alpha: number;

  /**
   * Primary constructor.
   * 
   * @since 1.0.0
   * 
   * @param aPrime
   * @param bPrime
   * @param cPrime
   * @param t
   * @param R
   */
  constructor( aPrime: number, bPrime: number, cPrime: number, t: number, R: number ) {
    this.aPrime        = aPrime;
    this.bPrime        = bPrime;
    this.cPrime        = cPrime;
    this.t             = t;
    this.halfThickness = t / 2;
    this.R             = R;
    this.alpha         = ! this.empty( cPrime ) ? 1.0 : 0.0;
  }

  /**
   * Final value in `in^4` units.
   * 
   * @since 1.0.0
   */
  public get value() {
    const partOne = Math.pow( this.t, 3 ) / 3,
          partTwo = ( this.a + ( this.b * 2 ) + ( this.u * 2 ) + this.alpha * ( ( this.c * 2 ) + ( this.u * 2 ) ) );

    return partOne * partTwo;
  }

  /**
   * Inner-bend radius.
   * 
   * @since 1.0.0
   */
  public get r() {
    return this.R + this.halfThickness;
  }

  /**
   * Parameter `a`.
   * 
   * @since 1.0.0
   */
  public get a() {
    return this.aPrime - ( 2 * this.r + this.t );
  }

  /**
   * Parameter `b`.
   * 
   * @since 1.0.0
   */
  public get b() {
    return this.bPrime - ( this.r + this.halfThickness + this.alpha * ( this.r + this.halfThickness ) );
  }

  /**
   * Parameter `c`.
   * 
   * @since 1.0.0
   */
  public get c() {
    return this.alpha * ( this.cPrime - ( this.r + this.halfThickness ) );
  }

  /**
   * Parameter `u`.
   * 
   * @since 1.0.0
   */
  public get u() {
    return Math.PI * this.r / 2;
  }

  /**
   * Lodash version of PHP's `empty` function.
   *
   * @link https://gist.github.com/DaveyJake/2096f3f7b09d26fcce25c1886e2571a0
   * @since 1.0.0
   * @access private
   *
   * @param value Value to check.
   *
   * @returns True if `value` is one of the conditions. False if not.
   */
  private empty( value: any | any[] ) : boolean {
    /**
     * Conditions we want to return as true.
     *
     * @since 1.0.0
     */
    let conditions: Array<boolean> | Array<number> = [
      _.isEqual( value, 0 ),
      _.isEqual( value, '0' ),
      _.isEqual( value, false ),
      _.isEqual( value, 'false' ),
      _.isEqual( value, '' ),
      _.isEqual( value, [] ),
      _.isEqual( value, {} ),
      _.isEqual( _.isNaN( value ), true ),
      _.isEqual( value, 'NaN' ),
      _.isEqual( _.isNull( value ), true ),
      _.isEqual( value, 'null' ),
      _.isEqual( _.isUndefined( value ), true ),
      _.isEqual( value, 'undefined' )
    ];

    // Convert boolean conditions to integers: true = 1; false = 0.
    conditions = _.map( conditions, _.toNumber );

    // Get the sum of the conditions.
    const result = _.sum( conditions );

    // If the result is greater than 0, we know it's empty.
    if ( result > 0 ) {
      return true;
    }

    return false;
  }
}