Design of Tall Buildings

7/30/2019 Design of Tall Buildings

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EAS 454 - Tall Building 4

Rigid-Frame Structures

Assoc. Prof. Dr. Taksiah A. Majid


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- Comprises parallel or orthogonally arranged bents consisting

o co umns an g r ers w momen res s an o n s.

The advantages of rigid frame are simplicity and convenienceof its rectan ular form. Its unobstructed arran ement, clear

of bracing members and structural walls, allows freedom

internally for the layout and externally for the fenestration.g rames are cons ere econom ca or u ngs o up

to about 25 stories, above which their drift resistance iscostly to control.

If it is combined with shear wall or cores, the structurespotential height may extend up to 50 stories or more.

slabs replacing the girders.


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Ri id-Frame Structures As highly redundant structures, rigid frames are designed initially

on the basis of approximate analyses, after which more rigorousana yses an c ec s can e ma e. e proce ure may yp ca y

include the following stages:


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Rigid-Frame Behavior The horizontal stiffness of a rigid frame is governed mainly

by the bending resistance of the girders, the columns,connec ons an e ax a r g y o e co umns.

The accumulated horizontal shear above any story of a rigidframe is resisted b shear in the columns of the stor .

The shear cause the story-height columns to bend in double

curvature with point of contra-flexure at approximately mid-- .


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Rigid-Frame Behavior The overall deflected shape of the rigid frame structure dueto racking has a shear configuration with concavity upwind, a

,

inclination at the top.

The overall moment of the external horizontal load is

resisted in each story level by the couple resulting from the

axial tensile and compressive forces in the columns onopposite si e o t e structure.


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- Because of the accumulative rotation up the height, the story drift

ue to overa en ing increases wit eig t, w i e t at ue to

racking tends to decrease.

The res onse of a ri id frame to ravit loadin differ from a

simply connected frame in the continuous behavior of the girders.

Negative moments are induced adjacent to the columns andpositive moments of usually lesser magnitude occur in the mid-

span regions.

The continuit also causes the maximum irder moments to be

sensitive to the pattern of live loading. This must be considered

when estimating the worst moment conditions.


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- For example, the gravity load maximum hogging moment adjacent

span and alternate other spans, as for A in the Fig. 7.3a. The maximum hogging moments adjacent to an interior column

to the column, as for B in Fig. 7.3b.

The maximum mid-span sagging moment occurs when live loadacts on the s an under consideration and alternate other s ans asfor spans AB and CD in Fig. 7.3a.


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- The dependence of a rigid frame on the moment capacity of

the columns for resisting horizontal loading usually causes

the columns of a rigid frame to be larger than those of the

.

On the other hand, while girders in braced frames are

desi ned for their mid-s an sa in moment, irders in ri idframes are designed for the end-of-span resultant hogging

moments, which may be of lesser value.

Consequent y, gir ers in a rigi rame may e sma er t an inthe corresponding braced frame.


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- Such reductions in size allow economy through the lower

cost of the girders and possible reductions in story height.

These benefits may be offset, however, by the higher cost of

.


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Approximate Determinate of Member

orce ause y rav y oa n

accurate analysis can be made only after the member sizes areassigned.

ere ore, mem er sizes are eci e on t e asis oapproximate forces estimated either by conservative formulas

of b sim lified methods of anal sis that are inde endent ofmember properties.

Three approaches for estimating girder forces due to gravity

1. Girder Forces Code RecommendedValues

2. Two C cle Moment Distribution

3. Column Forces


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.

In rigid frames with two or more spans in which the longer

of any two adjacent spans does not exceed the shorter by

more than 20% and where the uniformly distributed design

,

girder moment and shear may be estimated fromTable 7.1.

This summarizes the recommendations iven in the UniformBuilding Code.


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1.Girder Forces Code Recommended Values


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. It is for estimating girder moment in a continuous multi-bay

span an more accura e an e ormu as n a e .

especially for cases of unequal spans and unequal loading indifferent spans.

Assumption for the analysis:

1. A counterclockwise restraining moment on the end of ag r er s pos ve an a c oc w se momen s nega ve.

2. The ends of the columns at the floors above and below theconsidered irder are fixed.

3. In the absence of known member sizes, distribution factorsat each joint are taken equal to 1/n, where n is the

.


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wo yc e oment str ut on - or e examp e

A four-span girder AE from a rigid-frame bent is shown with its

loading.


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-

The fixed-end moments in each span are calculated for dead

oa ing an tota oa ing using t e ormu as given in ig. . .


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TwoCycle Moment Distribution - Worked example Example calculation of fixed-end moment for span AB.


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-

The moments for all spans are summarized as follows:

DE


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-

The purpose of the moment distribution is to estimate for

each support the maximum girder moments that can occur as

a result of dead loading and pattern live loading.

maximum moment at each support, and a distribution made

for each combination.


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TwoCycle Moment Distribution - Worked example

The moment distribution of each support are presented

separately as follows:


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wo yc e omen s r u on - or e examp e


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-

The complete set of operations can be combined as below:

1

4

6


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Maximum Mid-Span Moments


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-


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. The gravity load axial force in a column is estimated from the

accumu a e r u ary ea an ve oor oa ng a ove a

level, with reductions in live loading as permitted by thelocal Code of Practice.

The gravity load maximum column moment is estimated bytaking the maximum difference of the end moments in the

column ends just above and below the joint.

To this should be added any unbalanced moment due to

eccentricity of the girder connections from the centroid ofthe column, also allocated equally between the column endsabove and below the oint.


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Approximate Analysis of Member

orces ause y or zon a oa n

.

First step is to estimate the allocation of the externalhorizontal force to each bent.

It is usual to assume that the floor slabs are rigid in plane and

therefore, constrain the horizontal displacements of all the

translations and rotation of the floor slab.


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orces ause y or zon a oa n Symmetric Plan Structure Subjected to Symmetric Loading

The structure translate but does not twist.

From the assumption of slab rigidity, the bents translate

.

The total external shear at a level will be distributed between

the bents in proportion to their shear rigidities (GA) at thatlevel.


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orces ause y or zon a oa n Asymmetric Plan Structures

The effect of lateral loading on a structure having an

asymmetric plan is to cause a horizontal plane torque in

additional to transverse shear. Therefore the structure will

twist as well as translate.


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Referring to the asymmetric structure, and defining the

ocation o t e center o t e s ear rigi ity o t e set o para e

bents in story i, relative to an arbitrary origin 0, as given by


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orces ause y or zon a oa n

2. Member Force Anal sis b Portal Method

The portal method allows an approximate hand analysis forrigid frames without having to specify member size and

very useful for a preliminary analysis.

Most appropriate to rigid frames that deflectpre om nan y y rac ng.

Suitable for structures of moderate slenderness and height,

up to 25 stories in height with a height-to-width ratio not

greater than 4:1.


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Its name is derived from the analogy between a set of single-ay por a rames an a s ng e s ory o a mu - ay r g

frame. When each of the se arate ortals carries a share of the

horizontal shear, tension occurs in the windward columnsand compression in the leeward columns.


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If these are superposed to simulate the multi-bay frame, theax a orces o e n er or co umns are e m na e , eav ng an

axial forces only in the extreme windward and leewardcolumns.

The reduction of the highly redundant multistory frame toallow a simple analysis is achieved by making the following

1. Horizontal loading on the frame causes double curvaturebending of all the columns and girders, with points of

contraflexural at the mid-height of columns and mid-spanof girders.

-.the columns in proportion to the width of aisle each

column supports.


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Procedures are as follows:


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Member Force Analysis by Portal Method


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em er orce na ys s y or a e o The bending moment are recorded on the girders above the

left-hand end and below the right-hand end, and similarly on

the columns as viewed from the right.

beams at the mid-heights and mid-spans, respectively.

The bendin moment dia ram is drawn here on the tensionside of the member.

If member forces are required only at a particular level in the

structure, it can be analyzed separately by the aboveprocedure without having to start the analysis at the top (Fig.

.


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em er orce na ys s y or a e o The simplicity of the portal method and the advantage that it

allows a direct analysis of member forces at a intermediate

levels make it the most useful of the approximate method for- .

If, however, the frame is taller and more slender, so that

overall bendin of the structure b axial deformations of thecolumns becomes significant, it may be more appropriate to

analyze it by the cantilever method.


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e erm ne e mem er orces n e -s ory rame o g.

7.8.

m.

The bents are spaced at 7.0 m. The intensity of the wind loading is 1.5 kN/m throughout the

height.


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Solution:

Wind load per floor

s r u ng s s ear e ween e op-s ory co umns n

proportion to the widths of aisle supported:

Similarly for columns C and D.


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Starting with the top-left module A20 (Fig. 7.9a) and

consi ering its ree- o y equi i rium:


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Because of the mid-length point of contraflexure, the

moment at the right end of the girder has the same value as

at the left end.

,

story are equal.

The si n convention for numerical values of the bendinmoment is that an anticlockwise moment applied by a joint

to the end of a member is taken as positive.


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Continuing with the next module to the right, B20, in Fig.

7.9b:


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For the direct analysis of forces at an intermediate level,

consider floor level 8 (Fig. 7.8).

From moment equilibrium of the joint, moment at end of


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A i t A l i f M b


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orces ause y or zon a oa n3. Approximate Analysis by Cantilever Method

This method is based on the concept that a tall rigid frame

subjected to horizontal loading deflects as a flexural

. . .

Suitable for the analysis of structures of up to 35 stories

hi h with hei ht-to-width ratios of u to 5:1.

It is similar to the portal method in considering the

equilibrium of joint modules in sequence.

It differs, however, in starting by assuming values for theaxial forces, rather than the shear in the columns.

A i t A l i b C til


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Approximate Analysis by Cantilever

e o It is less versatile than the portal method in not allowing a

direct analysis of intermediate stories.

The assumption for cantilever method are as follows:

1. orizonta oa ing on t e rame causes ou e curvature

bending of all the columns and girders with points of

contraflexure at the mid-hei hts of columns and mid-s ansof girders.

2. The axial stress in a column in proportional to its distance

from the centroid of the column areas.



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e o The procedure for analysis is as follows:



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e o



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e o


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Analysis of the same 20-story, 70 m height frame considered

in the portal analysis.

Referring to Fig. 7.10, external moment due to wind are:


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Cantilever Method Worked Example


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Cantilever Method Worked Example


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an ever e o or e xamp e From moment equilibrium of joint, moment at top of

column


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Thank You.

Design of Tall Buildings

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