Understanding Stiffness Modification and AA' Beams in Structural Engineering

[fonseh]

Homework Statement

I don't understand why the stiffness for span have extension pin stated from original stiffness ... According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI / 4L , is the notes wrong ? And i don't understand what is AA' beam , can someone explain about it ? According to online notes , for the far end pin / roller , the k is 3EI / L but not 3EI / 4L , is the notes wrong ? And i don't understand what is AA' beam , can someone explain about it ?
. And I also don't understand why the span beam have extension pin is 3/4 from the original stiffness ? It's now shown in the notes ..

Homework Equations

The Attempt at a Solution

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I think the notes is wrong , it should be 3EI / 4L ..

 

[nilesh_pat]

For AA' beam , it's simply a beam with two supports , one end is fixed and another end is roller support. The stiffness for span beam with extension pin is 3/4 from the original stiffness because when the extension pin is added , the effective length of the beam will be shortened as the pin will be part of the beam. Therefore the stiffness of the beam will increase.