{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

L32_singularity functions-10 fall

# L32_singularity functions-10 fall - EAS 209-Fall 2010...

This preview shows pages 1–6. Sign up to view the full content.

EAS 209-Fall 2010 Instructors: Christine Human Lecture 32 Beam Deflection using Singularity Functions We can use singularity functions to solve for beam deflection by writing a single equation for w(x) and integrating four times. Today’s Homework: 12/20/2010 1 Lecture 32-Singularity Functions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EAS 209-Fall 2010 Instructors: Christine Human In the process of graphical integration we have seen that: Similarly, there will be a jump or “singularity” in the slope diagram at a hinge, due to rotation at the hinge. 12/20/2010 2 Lecture 32-Singularity Functions Concentrated load Jump or “singularity” in shear diagram Kink (change in slope) in moment diagram Concentrated moment Jump or “singularity” in moment diagram No change in shear diagram
EAS 209-Fall 2010 Instructors: Christine Human Normal integration requires the function to be smooth and continuous between the limits. Singularity functions allow us to handle discontinuities with a single equation for the entire beam, and to integrate across these jumps and kinks (discontinuities). Family of singularity functions STEP FUNCTION RAMP In general n a x - is a singularity function defined as: For x<a 0 = - n a x For x≥a n n a x a x ) ( - = - 12/20/2010 3 Lecture 32-Singularity Functions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EAS 209-Fall 2010 Instructors: Christine Human The pointed brackets (Macaulay’s brackets) are like ordinary brackets except that they are blind to negative quantities (and negative exponents). n n a x a x a x a x a x - - - - - - - 1 0 1 , , ..... are all singularity functions A useful feature of singularity functions is that the brackets < > can be differentiated and integrated as ordinary parentheses provided n ≥0 Integration - + = - + 0 1 1 1 n a x n dx a x n n Differentiation 0 1 1 - + = - + n a x n a x dx d n n 12/20/2010 4 Lecture 32-Singularity Functions
EAS 209-Fall 2010 Instructors: Christine Human However, if n <0 the function simply integrates by increasing the exponent by one.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}