What is the Influence Line for a Beam Supported at a Roller?

[fonseh]

Homework Statement

In part a , the author state that at the roller , it will restrain the beam from moving vertically , so the beam wouldn't deflect at roller at part a ... But at b , the author showed that the beam will deflect at roller , why is it so ?

Homework Equations

The Attempt at a Solution

IMO , the beam can't deflect at the roller in example b . so there's no influence line at the region between the roller and the pin [/B]

 

[CivilSigma]

In figure b) , that is an internal hinge, not a roller support. Internal hinges allow the beam to rotate about them.

 

[fonseh]

In figure b) , that is an internal hinge, not a roller support. Internal hinges allow the beam to rotate about them.

yes , there's internal hinge , it will allow rotation , but on the other end , it's an roller , roller wouldn't allow rotation , right ? So , the beam which connected to the right part of the hinge can't deflect as shown by the author , right ??

Although there's an internal hinge that will allow rotation , but the roller would not allow roattion , so th beam can't deflect as shown , right ?

 

[CivilSigma]

The roller here acts as a pivot point for the beam segment from the internal hinge to the rollers at C.

For positive convention as drawn for the guided roller motion at C, the beam segment from the internal hinge up to the guided roller will move as a whole, pivoting about the roller support.

 

[fonseh]

The roller here acts as a pivot point for the beam segment from the internal hinge to the rollers at C.

For positive convention as drawn for the guided roller motion at C, the beam segment from the internal hinge up to the guided roller will move as a whole, pivoting about the roller support.

The problem is the shear force is applied at B ( which is closer to the roller at C rather the hinge) , so the roller at C will determine whether the beam will deflect upwards or not ... So, since the roller resist the upwards motion of the beam , so the beam wouldn't deflect updwards , am i right ?

 

[CivilSigma]

So, since the roller resist the upwards motion of the beam

I don't really understand what you mean. If your in doubt, just take a virtual load , apply it on the beam, and manually find the shear force at B.

If you put the unit load at the roller, you will find that shear at B is 0 . If you put the load to the left of the roller, Assuming positive force direction is downwards, you will find that the shear force is some positive value and to the right of the beam some negative value.

 

[fonseh]

do

you will find that the shear force is some positive value and to the right of the beam some negative value.

Do you mean at the roller the shear force isn't 0 , but negative value of the force applied ?

 

[CivilSigma]

Sorry, I meant to the right and left of the roller.

Placing the unit load directly on the roller means that the reaction support at the roller is 1. So , there won't be any shear force any where else on the beam.

 

[fonseh]

Sorry, I meant to the right and left of the roller.

Placing the unit load directly on the roller means that the reaction support at the roller is 1. So , there won't be any shear force any where else on the beam.

What do you mean ? Can you explain it further ? What is the shear force exactly at the support(roller) , to the left and to the right of the beam ?