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wind are considered as well as those from live and dead load. The two extremes
of prirna'y axial stress, after the bridge is erected, are P4+Pal and P1;-Par:
where P.‘ is the maximum compression in the member from live load, its impact
and wind, and Pa numerically the maximum tension for the same loads. The
friction moments corresponding to the two extremes of stress then are u p (Pd+ P,i)
and 11 p (I’,,-P,g). When the coehicient of friction it has reached the amount
necessary to prevent further rotation on the pin, the turning momentsl
coexisting with the two extremes of primary axial stress are ‘considered equa
to the corresponding friction moments given above: H3-v the l“Ct‘0“ moment at
the pin is the limit of the turning moment in the member.
The total change in primary axial stress 15 (Pa+Po1)‘(Pd"Pa’) 'i1P“‘J;i:“i’S'
and the total change. Cr... in turning moment from one extremeel tolt go. V u
that due to the total change in its primary axial stress; 01'. Stilt , 3 E9 Val‘-'3 Y’
the sum (‘T,,,=u p (P,,+Pui) “"17 (1'.i‘,Pa?) =1‘? (P"‘+P"’)' “x 1? the Segon tiling
unit stress corresponding to the maximum. livehloady cgmpression an y :1
corresponding to the maximum live load tension. t en “e 3V0
.5 = Iii’ and x+y=5
y 1’.x"‘P42
secondary unit stress due to the maximum
Where S is the total change of r the bridge is erected. The above equations
change in primary axial stress afte
give
.E!’.a1..
=2P,,+P.i- .2
- 5 where S is found from the moment equation
”2P,,+P.,.-P..2 ’
(‘Tm=u [J (P,i+P..2)-
x
"lever arms are not
f the members of the canti
The 5CC0Tld3TY Stresses for mnst 0 .. t] e members P 2 reduces to the
affected by the load on the anCh".r 3?:-rfhdndoiii tiiees anchor arm 15.12 represents the
effect from wmd only‘ At the indfmllp loaded and the main span unloaded: Pu
Stresses when the afichor ‘fm-I limuisyunloaded and the main span fully loaded,
the $795595 whe“ 1 e anmor H - ' - d d Fxcessive secondary stresses in
the wind stresses In each 9359 bc.mg -mdu C ' icall indeterminate Drin1al'Y
th t' l posts above the main P1975. and Stat y f d. t blc length.‘ for
e ver ica ' g i , -d d by mcanso a ]US a >
Stresses m an adlacem memberbi “ilresifhfihge Connections for the false chords
the sub-cliords A M12 - M14, an
QM 14- Al 16- ndary 51,-gsscs due to the elastic deforma-
. 0 -
Impact and wind also Pmduce Sec
. ‘ > ediate points of
, these stresses for the intcrm . .
“on of the truss as a whole" To find of the cantilever and anchor arms. it is
‘ . I
the bottom Chords and en'd dlaiiiiiiilg Stilt: maximum primary’ stresses. fTi) She
heCC553"Y to use me ioadmgg d are added those produced bY ‘he "CH0"
SCC0“d3TY SWCSSCS. thfus flgtiianrfje wading, The sum gives the total secondary
moments at the pins or . ts
stresses at the intermediate P3“! pm" . d of Slide
d that the members may mu lilstma void the
dvance - , 0 3
The theory has been a b tum a sufhcient amoun .
on the pins and that they tifiizn iiieereid: which result from a large coefhcgzictnvig
large secondary Stress“? at pthis is undoubtedly true. but the Wins?‘ h .
friction. For SW13“ ““‘tG5.l‘lr?SSc5 Appendix XI-9) show a lenglllepflng 0 the
by Prof‘ MaCKay of MC I is?" d a narrowing Of about oncg-ha as muc wl ,
hob-35 of eycbgrs of about 0.211 unit Stresses of usual practice. The measure
pins only 5” in diameters an
161
merits of the stress in the front of the pins of compression members made by Mr.
James E. Howard (see Appendix XI-4) also show large deformations of the pin
holes with usual unit stresses in the members. As soon as the pin fits the de-
formed hole no further rolling can take place; all turning must then be by sliding.
If the pins had not been lubricated it is probable that the bending moments
at the pins under maximum stresses would have been approximately the same as
those which would obtain if the connections had been riveted up in the shop
without the members being restrained in any way. The bending moments
would have been those due to deformations from dead, live, impact. and wind
stresses. The lubrication of the pins is therefore useful even if it does not per-
manently reduce the pin friction. It is also doubtful whether the effect of
paraffin lubrication will ever, during the lifetime of the bridge, so completely
disappear as to give a coefficient 11 of 0.40; but since this cannot be substantiated
by evidence it seemed advisable to assume this friction coefficient, especially
since the assumption affected only a few joints of the bridge.
The results of the calculation of the secondary stresses in the cantilever and
anchor arms. as well as the additions made to the sections to provide for the
secondary stresses, are shown graphically on Plates LVII and LXIX, Volume II.
These also show the details of the calculation and the additions made to the
sections to provide for the secondary stresses.
IIA. 01 Stresses in the Posts and Suspenders of the Suspended Span
“'hen long floorbeams are riveted to posts or suspenders the latter bend to
an appreciable inclination from the vertical as live load comes on the beam. In
order to make this inclination a minimum for such members the connection angles
were so faced that these supporting members are vertical under a half live load
with its impact. The inclination under maximum live load is then as much one
way as the inclination is the other way when there is no live load on the beam.
The posts and suspenders are, therefore, under equal but opposite bending
stresses for full live load and no live load, and this bending stress is less than half
what it would have been if the connection angles had been made vertical for no
load.
VVhat is required is to find the bending moment in the post in terms of the
angle of inclination at the connection. Since in this case the floorbeam is stiff in
comparison with the post. it will be practically correct to assume the inclination
equal to the tangent of the elastic line at the end of the fioorbeam as found for
one-half live load and its impact the Hoorbeam assumed as hinged at the end,
and this tangent is easily obtained. The effect of z
axial stress in the member on its bending moment at
the connection is neglected.
In the accompanying sketch (Fig. 1) Mo repre-
sents the moment to be found, 1.; is the length of the
hanger up to the intermediate cross strut, I; the length
from the intermediate cross strut to the deeper top
cross strut, at the end of which the hanger is con-
sidered fixed and vertical in position. No moment
restraint is assumed offered by the intermediate
cross strut at 111). awill be used as tan a in the
calculation. Then between R0 and R; we have
M,=Rox+ilIo, (1)
And between R . and R2 we have
M,=Rox+.7lIo+R; (x-Io). (2)