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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 SpecificationSection of the Manual . However, this table will not work very well with rigid frames. Columns ina frame are not independent, they are continuous. The buckling of one member will affect all the members aroundit. Therefore, the end conditions necessary for using Table C-C2 are not sufficient. It is important to account for thedegree 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 havesidesway.

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

G E c I c L c E g I g L g I c L c I g L g

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

G and k relationships

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

"The relationship between G and K 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 K from one of the nomograms, first calculate the value of G at each end of the column, letting one value be G A and the other be G B . Connect G A and G B with a straight line, and read the value of K on the middle scale. The effective length factor obtained in this manner is withrespect to the axis of bending, which is the axis perpendicular to the plane of the frame. A separateanalysis must be made for buckling about the other axis. Normally the beam-to-column connections in this directionwill not transmit moment, sidesway is prevented by bracing, and K can be taken as 1.0.

Value of g for pinned support

G can be taken as 10 at a pinned support because at a pin connection, the situation isjust like a very stiff column attached to infinitely flexible girders. This means the girders have zerostiffness. Then, the ratio of column stiffness to girder stiffness would be infinite for a perfectly frictionlesshinge. This end condition can only be approximated in practice, so the discussion accompanying the alignment chartrecommends that G be taken as 10.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
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can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
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Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
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Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Steel design (civi 306). OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10153/1.3
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