Handbook of Frame Constants PCA

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Handbook

of frame constants

P0RTLAND CEMENT

ASSOCIATI0N

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HANDBOOK OF

FRAME CONSTANTS

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Handbook of Frame Constants Beam Factors and Moment Coefficients

for Members of Variable Section

The activities of the Portland Cement Association, a national organization, are limited to scientific research, the development of new or improved products and methods, technical service, promotion and educational effort (including safety work), and are primarily designed to improve and extend the uses of port land cement and concrete. The manifold program of the Association

and its varied

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services to cement users are made possible by the financial support of over 60 member companies in the United States and Canada, engaged in the manufacture and sale of a very large proportion of all port land cement used in these two countries. A current list of member companies will be

furnished on request.

COPYR1GHT, l»47bY PORTLaNDCEMENTaSSOC1aT1ON

Published by

PORTLAND CEMENT ASSOCIATION 33 West

Grand Avenue

•

Chicago 10,

Illinois

NOMENCLATURE ratio of length of haunch at end A to length of span ratio of length of haunch at end 8 to length of

oA

=

ob

=

b

=

ratio of distance from loading to length of span

=

ratio of distance from loading point to end B to length of span

span

bt

point to end A

CAb

=

carry-over factor of member AB at end A

CbA

=

E

=

ru

=

ha

=

factor of member AB at end B of elasticity depth of member at end A depth of member at end B depth of member at minimum section moment of inertia of section of minimum depth moment of inertia of any section distance x from A or X! from B stiffness factor of member AB at end A; stiffness

hc

=

U

=

fx

=

JcAb

=

carry-over modulus

= kuEU

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L

ktA

=

stiffness

L

=

length of member

MAb

=

fixed end moment at end A of member AB for any type of loading; used to identify column of F.E.M. coefficients in tables

Msa =

fixed end moment at end B of member AB for any type of loading; used to identify column of F.E.M. coefficients in tables

factor of member AB at end B

P

=

tA

=

rt

=

w

=

uniform

WA

=

weight of haunch per lin.ft. right at end A

concentrated load ^c he ^c nc

for rectangular

cross-section

for rectangular cross-sectton

at end A at end B

load

Wt

=

weight of haunch per lin.ft. right at end B

x

=

distance from variable

point to end A

=

distance from variable

point to end B

X]



0

Carry-over Factors

1

L

lJ

*

All carry-overfactorsare negative and all stiffnessfactorsare positive.

AH carry-overfactorsand fixed end momentcoefficientsare negative and all stiffnessfactorsare positive.

1 I 00

H

-Constant

bL

0 1

l

qL

X

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0.2

Mba

0 1

2.0

0.499 498 497 496 0.495

1 5

0.4 0.6 1.0

Ma

0

"a3

I

9.57 19.91 26.69 43.68 71.76 10800

0

5.57 6.96 7.63 8.92 10 48 12.00

0

0.641 0.373 0;837 0.292 0.929 0.265 1.103 0.225 1.307 0.191 1 500 0.167

Depth

Concentrated LoadF.E.M.— Coef. X PL

Unif. Load F.E.M. Coef. taL'

Stiffness Factors

0

0.0 0.4 0 6 1.0

Carry-over Factors

00

8.23 17.20 23.09 37.91 62.50 94.34

0833 0841 0854 0867 0876

All carry-overfactorsand fixed end momentcoefficientsare negative and all stiffnessfactorsare positive.

000

5.23 6.57 7.22 8.48 10.00 11.48

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|

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S|Ej634.ui

Oo| (-ui)

(.b+l)6o|

U94M .b*J

82

xpx

xp2x

xpx

|

/

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It —m— /ET

^P?

(R-b4|)£(Rj4|)I^I

|

J

j+2

|

t>j

(J»l)6o|

2t> (.bt|)6o|

°I

|

j

2+

fo-j) z[j*\)z

| J (J*|)Boi t)-J2 J zCb-j)j tCb-J)tJ4|

"b (t>+|)60| t(t»-J) .b

U8MM

qi

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qe

*P

T

xpx

L

xpx

xpzx

|

XPyX

Q31N1Ud Nl n "S 'V

/

HP

£i /

npn

fl

J

£+

—Lt-9 tt-±W-O1—

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