# Angle of rotation in fixed end of beam

In the first photo, i was told that the fixed end moment is zero when the far end is pinned or roller supported . Why in the example in the second and third photo( both end are fixed) , the angle is zero ?

I think it's wrong , because the fixed end must be able to resist shear force . In conjugate beam method , angle of rotation = shear force . So , as the fixed end can resist the moment , there must be some values for the angle if rotation , am i right ?

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• What do the second and third images (in color) have to do with the question? Why did you upload them? As I understand it, your question is about the first image (black-and-white), correct? And the "moments at A and D are zero" seems to be about Figure 11-9, where A and D are pinned supports, not fixed. Therefore they have zero moment reaction. – Wasabi Jan 14 '17 at 11:37
• @Wasabi , pls refer to the edited post , photo 2 . I have circled the part where the author stated the theta( angle of rotation) is zero for fixed support . How can that be true ? In the first post , i was told that at the pinned and roller support , then the theta is zero . Why for fixed support , the theta( angle of rotation) is also zero ? – kelvinmacks Jan 14 '17 at 11:48
• @Wasabi , one mpre question , how do we know whether the theta represent the angle due to moment ? Or shear force ? – kelvinmacks Jan 14 '17 at 11:55

## 1 Answer

Ok. Yeah.

Your question seems to be why a fixed support has zero rotation ($\theta=0$). The answer is simple: that's the definition of a fixed support. Here is a table representing the constraints placed by different types of supports (for a 2D frame structure, of course):

Support       | dX | dY | rZ |
--------------+----+----+----+
Pinned        | X  | X  |    |
Fixed         | X  | X  | X  |
Plate         |    |    | X  |
Roller*       | *  | *  |    |
Fixed roller* | *  | *  | X  |
(* one or the other)


So, pinned supports do not allow any sort of translation (dX, dY), but do allow rotation (rZ). Fixed supports do not allow any translation or rotation. Plate supports (I don't know of a better name for them) allow translation but no rotation. Roller supports allow for rotation and for translation in one direction but not the other. Fixed rollers are the same, but don't allow rotation.

The first circle you drew states that a pinned or roller support does not resist bending moments and therefore allows rotations ($M_R = 0 \therefore \theta \neq 0$). A fixed support, on the other hand, does not allow rotations and therefore generates a resisting bending moment ($\theta = 0 \therefore M_R \neq 0$).

In a comment under your question you state that "In the first post, i was told that at the pinned and roller support, then the theta is zero." I don't know if this was a reading mistake on your part (since the author clearly states that the bending moment is zero, not $\theta$) or if you simply don't know the difference between them. Hopefully it is the former, because the latter would be such a fundamental misunderstanding that I simply won't be able to help you.

The second circle you drew states that "moments at A and D are zero". Looking at Figure 11-9, we can see that A and D are pinned supports at the extremities of the beam, so yeah, by definition we know that the moments at A and D are zero.

The third circle you drew states that "$\theta_A = \theta_D = 0$ since A and D are fixed supports." Given the definition, no further explanation should be necessary.