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Mechanics Library

Mechanics. Simple beam. Uniformly distributed load. End slopes

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

General information

Procedure BeamType1_UDL_EndSlopes calculates slopes [rad] 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:

\[S_a = -w \frac{L^4 - 4 L^2 a^2 - 2 L^2 b^2 + 4 L a^3 - a^4 + b^4}{24 E I L} \]

\[S_b = w \frac{L^4 - 2 L^2 a^2 - 4 L^2 b^2 + 4 L b^3 + a^4 - b^4}{24 E I L} \]

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];
  • Sa, Sb — radians [rad].

DLL

dystlab.mechanics.dll

Usage format (Pascal)

procedure BeamType1_UDL_EndSlopes(w, a, b, L, E, I: Double; var Sa, Sb: 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];
  • Sa — slope at support A [rad];
  • Sb — slope at support B [rad].

Return value

Procedure returns in Sa, Sb correspondent slopes [rad]. If errors (for example, L<0), procedure returns Sa=0 and Sb=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_EndSlopes(w, a, b, L, E, I: Double; var Sa, Sb: Double); stdcall; external 'dystlab.mechanics.dll';

var
Sa, Sb: Double;

begin
BeamType1_UDL_EndSlopes(1.5, 0, 0, 2.0, 15.0e9, 5.2e-9, Sa, Sb); ShowMessage(Format('Sa=%1.5f', [Sa]) + '; ' + Format('Sb=%1.5f', [Sb])); end;

See also

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