Tag Archives: Cubic spline

Continuous beam with varying stiffness

Posted on 23/08/2009 by dougaj4

Previous Splinebeam post One of my aims in developing the splinebeam function is to carry out non-linear analysis of reinforced concrete beams, allowing for the greatly reduced flexural stiffness of reinforced concrete sections after cracking of the concrete.  To that … Continue reading →

Posted in Arrays, Beam Bending, Excel, Finite Element Analysis, Maths, Newton, UDFs, VBA | Tagged , , , , , , , | 3 Comments

Continuous beam with specified end conditions …

Posted on 09/08/2009 by dougaj4

… and/or support displacements. The previous post in this series derived cubic splines with specified end conditions; either a specified curvature or a specified end slope. I have adapted the splinebeam function to allow input of specified end conditions (either a … Continue reading →

Posted in Arrays, Beam Bending, Excel, Finite Element Analysis, Frame Analysis, Maths, Newton, UDFs, VBA | Tagged , , , , , , , | 1 Comment

More on cubic splines

Posted on 12/07/2009 by dougaj4

Link to Cubic Spline Update The previous two posts used cubic splines with the “natural” end condition, that is with an end curvature of zero.  To apply the cubic spline to analysis of continuous beams with different end conditions we … Continue reading →

Posted in Beam Bending, Excel, Frame Analysis, Maths, Newton, UDFs, VBA | Tagged , , , , | 10 Comments

Continuous beam analysis with cubic splines

Posted on 05/07/2009 by dougaj4

The last example in the previous post illustrated the use of cubic splines to find the bending moments in a continuous beam subject to prescribed lateral displacements.  A similar technique can be used to find bending moments, shear forces, reactions, … Continue reading →

Posted in Arrays, Beam Bending, Excel, Finite Element Analysis, Frame Analysis, Maths, Newton, UDFs, VBA | Tagged , , , , , , , | 9 Comments

Cubic Splines

Posted on 02/07/2009 by dougaj4

Cubic splines are used to fit a smooth curve to a series of points with a piecewise series of cubic polynomial curves.  In addition to their use in interpolation, they are of particular interest to engineers because the spline is … Continue reading →

Posted in Beam Bending, Excel, Newton, UDFs, VBA | Tagged , , , , | 73 Comments