30 - analysis of moment resisting frame and lateral load

7/21/2019 30 - Analysis of Moment Resisting Frame and Lateral Load

http://slidepdf.com/reader/full/30-analysis-of-moment-resisting-frame-and-lateral-load 1/8



foundation. &n bridges, these frames resist the forces caused b wind, earth'uae, and

unbalanced traffic loading on the bridge dec. +ortals can be pin supported, fi!ed supported, or

supported b partial fi!it. The appro!imate analsis of each case will now be discussed for a

simple threemember portal.

P!"#S$%%orted Portal* " tpical pinsupported portal frame is shown in #ig. (a). -ince four

unnowns e!ist at the supports but onl three e'uilibrium e'uations are available for solution, this

structure is staticall indeterminate to the first degree. onse'uentl, onl one assumption must be

made to reduce the frame to one that is staticall determinate.

The elastic deflection of the portal is shown in #ig. (b). This diagram indicates that a point of

inflection, that is, where the moment changes from positive bending to negative bending, is located

appro!imatel at the girder/s midpoint. -ince the moment in the girder is zero at this point, we can

assume a hinge e!ists there and then proceed to determine the reactions at the supports using

statics. If this is done, it is found that the horizontal reactions (shear) at the base of each column

are e'ual and the other reactions are those indicated in #ig. (c). #urthermore the moment

diagrams, for this frame, are indicted in #ig. (d).

http://theconstructor.org/category/geotechnical/foundations/

http://theconstructor.org/category/structures/

http://theconstructor.org/category/geotechnical/foundations/

http://theconstructor.org/category/structures/



#ig. +ortal frame pinsupported at base

F!ed#S$%%orted Portal: +ortal with two fi!ed supports, #ig. 0(a) are staticall indeterminate to

the third degree since there is a total of si! unnowns at the supports. If the vertical members have

e'ual lengths and crosssectional areas the frame will deflect as shown in #ig. 0(b). #or this case,



we will assume points of inflection occur at the midpoints of all three members, and therefore

hinges are placed at these points. The reactions and moment diagrams for each member can

therefore be determined b dismembering the frame at the hinges and appling the e'uations of

e'uilibrium to each of the four parts. The results are shown in #ig. 0(c). Note that, as in the case of

the pinconnected portal, the horizontal reactions (shear) at the base of each column are e'ual. The

moment diagram for this frame is indicted in #ig. 0(d).

#ig. 0 "nalsis of portal frames 1 #i!ed at base

Part!all' F!ed (at the Bottom) Portal: -ince it is both difficult and costl to construct a perfectl

fi!ed support or foundation for a portal frame, it is a conservative and somewhat realistic estimate

to assume a slight rotation to occur at the supports, as shown in #ig. 3(a). "s a result, the points of

inflection on the columns lie somewhere between the case of having a pinsupported portal (as

shown in #ig. (a)), where the 2inflection points are at the supports (base of columns), and that of a

fi!edsupported portal (as shown in #ig. 0(a)), where the inflection points lie at the center of the



columns. 4an engineers arbitraril define the location at h53 (#ig. 3(b)), and therefore place hinges

at these points, and also at the center of the girder.

#ig. 3 +ortal frame partiall fi!ed at base

Tr$ed Frame* 6hen a portal is used to span large distances, a truss ma be used in place of

the horizontal girder. -uch a structure is used on large bridges and as transverse bents for large

auditoriums and mill buildings. " tpical e!ample is shown in #ig. 7(a). In all cases, the suspended

truss is assumed to be pin connected at its points of attachment to the columns. #urthermore, the

truss eeps the columns straight within the region of attachment when the portals are subjected tothe sideswa 8, #ig. 7(b). onse'uentl, we can analze trussed portals using the same

assumptions as those used for simple portal frames. #or pinsupported columns, assume the

horizontal reactions (shear) are e'ual, as in #ig. (c). #or fi!edsupported columns, assume the

horizontal reactions are e'ual and an inflection point (or hinge) occurs on each column, measured

midwa between the base of the column and the lowest point of truss member connection to the

column. -ee #ig. 0(c) and #ig. 7(b).

http://theconstructor.org/category/structural-engg/truss/

http://theconstructor.org/category/structural-engg/truss/



#ig. 7 Trussed frame fi!ed at base

9ateral loads on :uilding #rames* +ortal #rame 4ethod

The action of lateral loads on portal frames and found that for a frame fi!ed supported at its base,

points of inflection occur at appro!imatel the center of each girder and column and the columns

carr e'ual shear loads, #ig. 0. " building bent deflects in the same wa as a portal frame, #ig.; (a),

and therefore it would be appropriate to assume inflection points occur at the center of the columns

and girders. If we consider each bent of the frame to be composed of a series of portals, #ig. ; (b),

then as a further assumption, the interior columns would represent the effect of two portal columns

and would therefore carr twice the shear < as the two e!terior columns.

onsider the 08 frame with mbase and nstores. The degree of indeterminac of the frame is

3mn. To analze the frame, 3mn assumptions are made=

• The point of contrafle!ure in the column is at midheight of the columns* (m>)n assumptions.

• The point of contrafle!ure in the beams is at the mid span of the beams* mn assumptions.

• "!ial force in the internal columns is zero (m>)n assumptions.

• 6ith the above assumptions, the frame becomes staticall determinate and member forces are

obtained simpl b considering e'uilibrium.



B. *a"t!le+er method: In this method also, 3mn assumptions are to be made to mae the frame

staticall determinate= the point of contrafle!ure in the column is at midheight of the columns*

(m>)n assumptions.

• The point of contrafle!ure in the beams is at mod span of the beams* mn assumptions.

• "!ial force in the columns is appro!imated b assuming that the frame behaves as a cantilever

beam. Neutral a!is of the frame is obtained using the column area of cross section and the column

location, a!ial stress in the column is assumed to var linearl from this neutral a!is* (m)n

assumptions.

The cantilever method is based on the same action as a long cantilevered beam subjected to a

transverse load. It ma be recalled from mechanics of materials that such a loading causes a

bending stress in the beam that varies linearl from the beam/s neutral a!is, #ig. ? (a). In a similar

manner, the lateral loads on a frame tend to tip the frame over, or cause a rotation of the frame

http://theconstructor.org/category/structural-engg/solid-mechanics/

http://theconstructor.org/category/structural-engg/solid-mechanics/



about a 2neutral a!is ling in a horizontal plane that passes through the columns at each floor level.

To counteract this tipping, the a!ial forces (or stress) in the columns will be tensile on one side of

the neutral a!is and compressive on the other side as in #ig below. 9ie the cantilevered beam, it

therefore seems reasonable to assume this a!ial stress has a linear variation from the centroid of

the column areas or neutral a!is. The cantilever method is therefore appropriate it the frame is tall

and slender, or has columns with different crosssection areas.

30 - analysis of moment resisting frame and lateral load

Documents