Parameters are missing. Displacement Method of Analysis: Moment Distribution

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Chapter:

6. Required Moment that is to be applied at end A to produce unit rotation if far end is hinged is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is hinged is _\r\n\r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) \(\frac{4EI}{L} \)

\(\frac{3EI}{L} \)

If a unit rotation is to be caused at an end A for far end being hinged support. Moment of \(\frac{3EI}{L} \) is to be applied at end and hence stiffness for member is said to be \(\frac{3EI}{L} \).

Hint Answer

7. Required Moment that is to be applied at both ends to produce unit rotation on both simply supported support is _

$Required Moment that is to be applied at both ends to produce unit rotation on both simply supported support is _\r\n \r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) \(\frac{4EI}{L} \)

\(\frac{2EI}{L} \)

If a unit rotation is to be caused at an end A for far end being hinged support. Moment of \(\frac{2EI}{L} \) is to be applied at end A and B and hence stiffness for member is said to be 2EI/L.

$Required Moment that is to be applied at both ends to produce unit rotation on both simply supported support is _____\r\n \r\n$

Hint Answer

8. Stiffness of end A if far end B is vertical guided roller is

$Stiffness of end A if far end B is vertical guided roller is \r\n\r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) \(\frac{4EI}{L} \)

\(\frac{EI}{L} \)

If a unit rotation is to be caused at an end A for far end being vertical guided roller support. Moment of \(\frac{EI}{L} \) is to be applied at end A and hence stiffness for member is said to be \(\frac{EI}{L} \).

Hint Answer

9. Stiffness of end A if far end B is free is

$Stiffness of end A if far end B is free is \r\n\r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) 0

0

As free end cannot resist any moment nor can support any vertical or horizontal reactions. End support B cannot take any portion of moment applied at end A. Thus, stiffness for member would be zero.

Hint Answer

10. Required Moment that is to be applied at end A to produce unit rotation if far end is vertical roller support as shown in figure is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is vertical roller support as shown in figure is _\r\n\r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) \(\frac{4EI}{L} \)

\(\frac{3EI}{L} \)

If a unit rotation is to be caused at an end A for far end being roller support. Moment of \(\frac{3EI}{L} \) is to be applied at end and hence stiffness for member is said to be \(\frac{3EI}{L} \).

Hint Answer

11. Required Moment that is to be applied at end A to produce unit rotation if far end is horizontal roller support as shown in figure is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is horizontal roller support as shown in figure is _\r\n\r\n$

\(\frac{EI}{L} \) \(\frac{2EI}{L} \) \(\frac{3EI}{L} \) 0

0

Since horizontal roller support does not provide any restraint to vertical loading if moment is applied at that end. The end will simply slide down and hence would not resisting any portion of applied moment.

Hint Answer

12. Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

\(\frac{11EI}{L} \) \(\frac{13EI}{L} \) \(\frac{7EI}{L} \) \(\frac{8EI}{L} \)

\(\frac{8EI}{L} \)

Joint O is connected to four-member OA, OB, OC, and OD where far end is supported by vertical guided roller, vertical roller support, fixed support, and horizontal roller support respectively.
Stiffness for OA is \(\frac{EI}{L} \)
Stiffness for OB is 0
Stiffness for OC is \(\frac{4EI}{L} \)
Stiffness for OD is \(\frac{3EI}{L} \)
Therefore stiffness for joint O is sum of stiffness for all members connected to it.
Stiffness for joint O is \(\frac{EI}{L}+0+\frac{4EI}{L}+\frac{3EI}{L}=\frac{8EI}{L} \)

Hint Answer

13. Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

\(\frac{10EI}{L} \) \(\frac{6EI}{L} \) \(\frac{9EI}{L} \) \(\frac{8EI}{L} \)

\(\frac{8EI}{L} \)

Joint O is connected to four-member OA, OB, and OD where far end is supported by vertical guided roller, fixed support, and hinged support respectively.
Stiffness for OA is \(\frac{EI}{L} \)
Stiffness for OB is \(\frac{3EI}{L} \)
Stiffness for OC is \(\frac{4EI}{L} \)
Therefore stiffness for joint O is sum of stiffness for all members connected to it.
Stiffness for joint O is \(\frac{EI}{L}+0+\frac{4EI}{L}+\frac{3EI}{L}=\frac{8EI}{L} \)

Hint Answer

14. Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

\(\frac{9EI}{L} \) \(\frac{10EI}{L} \) \(\frac{11EI}{L} \) \(\frac{14EI}{L} \)

\(\frac{9EI}{L} \)

Joint O is connected to four-member OA, OB, OC, and OD where far end is supported by vertical guided roller, fixed support, free end, and fixed support respectively.
Stiffness for OA is \(\frac{EI}{L} \)
Stiffness for OB is \(\frac{4EI}{L} \)
Stiffness for OC is 0
Stiffness for OD is \(\frac{4EI}{L} \)
Therefore stiffness for joint O is sum of stiffness for all members connected to it.
Stiffness for joint O is \(\frac{EI}{L}+0+\frac{4EI}{L}+\frac{4EI}{L}=\frac{9EI}{L} \)

Hint Answer

15. Distribution factor is ratio in which force sharing capacity of various members meeting at a rigid joint.

True False

False

Distribution factor is ratio in which moment sharing capacity of various members meeting at a rigid joint.

Hint Answer

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Topics

This Chapter consists of the following topics

Displacement Method of Analysis: Moment Distribution

Required Moment that is to be applied at end A to produce unit rotation if far end is hinged is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is hinged is _\r\n\r\n$

;

Required Moment that is to be applied at both ends to produce unit rotation on both simply supported support is _

$Required Moment that is to be applied at both ends to produce unit rotation on both simply supported support is _\r\n \r\n$

;

Stiffness of end A if far end B is vertical guided roller is

$Stiffness of end A if far end B is vertical guided roller is \r\n\r\n$

;

Stiffness of end A if far end B is free is

$Stiffness of end A if far end B is free is \r\n\r\n$

;

Required Moment that is to be applied at end A to produce unit rotation if far end is vertical roller support as shown in figure is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is vertical roller support as shown in figure is _\r\n\r\n$

;

Required Moment that is to be applied at end A to produce unit rotation if far end is horizontal roller support as shown in figure is _

$Required Moment that is to be applied at end A to produce unit rotation if far end is horizontal roller support as shown in figure is _\r\n\r\n$

;

Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

;

Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

;

Rotational stiffness at joint O for shown figure is _

$Rotational stiffness at joint O for shown figure is _\r\n \r\n$

;

Distribution factor is ratio in which force sharing capacity of various members meeting at a rigid joint.

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