Skip to content Skip to navigation

Connexions

You are here: Home » Content » Effective Length and Frames

Navigation

Recently Viewed

This feature requires Javascript to be enabled.

Effective Length and Frames

Module by: Michael Terk. E-mail the author

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: (Blank Abstract)

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

A different effective length for frames

Effective length can be found easily on isolated columns by using Table C-C2 in the Commentary of the Specification Section of the Manual. However, this table will not work very well with rigid frames. Columns in a frame are not independent, they are continuous. The buckling of one member will affect all the members around it. Therefore, the end conditions necessary for using Table C-C2 are not sufficient. It is important to account for the degree of restraint by connecting members of a column in a frame.

A frame can be unbraced or braced, where unbraced means horizontal displacement in possible. A frame can also have sidesway.

"The rotational restraint provided by beams, or girders, at the end of a column is a function of rotational stiffnesses of the members intersecting at the joint." LRFD Steel Design Second Edition -- William T. Segui, 1999. The restraint is proportional to EIL E I L .

G=∑ E c I c L c ∑ E g I g L g =∑ I c L c ∑ I g L g G E c I c L c E g I g L g I c L c I g L g (1)

KK, then depends on the ratio of column stiffness to the girder stiffness at each end.

G and K relationships

KK is relatively small when a slender column is connected to a girder of large cross section. This is because the girder effectively prevents rotation and acts as a fixed end. The GG value for this case is rather small too. KK (or GG) is relatively large when the ends of very stiff columns are connected to rather flexible beams. This is because the ends of the column can more freely rotate and approach the pinned condition.

"The relationship between GG and KK has been quantified in the Jackson-Mooreland Alignment Charts (Johnston, 1796), which are reproduced in Figure C-C2.2 in the Commentary. To obtain a value of KK from one of the nomograms, first calculate the value of GG at each end of the column, letting one value be G A G A and the other be G B G B . Connect G A G A and G B G B with a straight line, and read the value of KK on the middle scale. The effective length factor obtained in this manner is with respect to the axis of bending, which is the axis perpendicular to the plane of the frame. A separate analysis must be made for buckling about the other axis. Normally the beam-to-column connections in this direction will not transmit moment, sidesway is prevented by bracing, and KK can be taken as 1.0.

Value of G for pinned support

GG can be taken as 10 at a pinned support because at a pin connection, the situation is just like a very stiff column attached to infinitely flexible girders. This means the girders have zero stiffness. Then, the ratio of column stiffness to girder stiffness would be infinite for a perfectly frictionless hinge. This end condition can only be approximated in practice, so the discussion accompanying the alignment chart recommends that GG be taken as 10.

Content actions

Give Feedback:

E-mail the module author | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks