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Mechanics Library

Mechanics. Simple beam. Uniformly distributed load. Deflections

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Procedure calculates deflections in simple beam under uniformly distributed load. Support A is considered left, support B is right.

General information

Procedure BeamType1_UDL_Deflection calculates deflection [m] in simple beam. Support A is considered left, support B is right. You can use this routine in your applications and reports during linear static analysis.

TechEditor - Mechanics Library

General equations:

\[d(x) = -\theta_A x - \frac{R_A x^3}{6EI}, x \leq a; \]

\[d(x) = -\theta_A x - \frac{R_A x^3}{6EI} + \frac{w(x-a)^4}{24EI}, a < x < L - b; \]

\[d(x) = \theta_B (L - x) - \frac{R_B (L - x)^3}{6EI}, x \geq L - b. \]

Recommended units of measurement

  • a, b, L, Lw, x — meter [m];
  • w — newton per meter [N/m];
  • E — Pascal [Pa];
  • I — meter in 4th degree [m4];
  • d — meter [m].

DLL

dystlab.mechanics.dll

Usage format (Pascal)

procedure BeamType1_UDL_Deflection(w, a, b, L, E, I, x: Double; var d: Double); stdcall; external [DllName];

Parameters:

  • w — intensity of the unirformly distributed load [N/m];
  • a — distance between start point of the load and support A [m];
  • b — distance between end of the load and support B [m];
  • L — beam length [m];
  • E — modulus of elasticity [Pa];
  • I — moment of inertia (cross-sectional characteristic for bending) [m4];
  • x — coordinate of analyzed section (distance between support A and section with deflection) [m];
  • d — resultant deflection [m].

Return value

Procedure returns in d correspondent deflection [m]. If errors (for example, L<0), procedure returns d=0.

Directives

  • DllName — library name. If DLL included in installation pack, then DllName is 'dystlab.mechanics.dll'.

Example for TechEditor

Next code calls routine from DLL and shows standard message box. Code can be used in applications for TechEditor 1.0.7 and higher.

uses
Classes, Dialogs;

procedure BeamType1_UDL_Deflection(w, a, b, L, E, I, x: Double; var d: Double); stdcall; external 'dystlab.mechanics.dll';

var
d: Double;

begin
BeamType1_UDL_Deflection(1.5, 0, 0, 2.0, 15.0e9, 5.2e-9, 1.0, d); ShowMessage('d=' + FloatToStr(d)); end;

See also

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