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ai, Vv
A Tnesis Sutmitted to

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Mm I CHI GAL, AGRI CULT UhAL COLL # G

W. ©. Dow RE. H. Walser

Candidates for the Deper-- or

Bach2aler of Seience

4,
THESIS
The follewirg books were used thro'out the work as reference,

Ketchun's--Structural Fand Rook (S. H. B.)
Wrights'--Desipgnire cf Draw-Srars
hCLlitcer’seeRiret@ec Trecry of Engineering
otructures,

We are esvecially in’ebted to Frofecscr C. A. Melick for
trie series of lectures he fave us in yrepuratior, for the loan
of detail crawings, and for his sugrestions and helr during the

progiess of the work.

The Authors.

95505
TABLE OF CCNTENTS

Pages

List of Detail Drawings

Outline
Introduction

Digcussion

Tables

Tabulation of weight of members

Panel poirt Concentrations

Live load continuous Stress (continuous bean theory)

Live Load Simrle Span Stresses

True dead 10a¢ continuous Stresses&

Actual live loa¢ continuous Stresses

True live load continuous Stresses 100047 panel
Allowed unit compressive stresser

Conbinetions of Stresses

Unit change in length due to 1# load at Center

Maximum Unit Stresses

Plates

Marker diagram

Dead load cantilever stresses

Stresses cue to 1000# uplift

Left Reactions by continuous beam theory

Stresses due to 1# load at center

V1---T35
T36--T 37
T39
T40
T41
T42
T43
T44
T45
T45

T46

Pl
P2
P3
p4
PS
Typical Influence Lines
Williot Deformation diagram

Diagram skewing stresses

P6=P7
P8
l.
LIST OF DRAWINGS
American Bridge Co. Order Nos. C9213 and C9216

Two 257'-0" Riveted draw spans. One span over Old River
san Joaquin and Contra Costa Co. California. One span over

Midcle River San Joaguin Co. California.

SHEET INDEX

Sheet Dl---Stresses Destorsions & Deflections & Mach. Stresses
~-=24x 36
D2-e-Diagram of structural steel to be assemciled in sliop
with machinery---12x24
Bl---Masonry plans showing location of bearings---24x36
B2---Brection diagram for structural steel---24x}36
E3---Erection diagram of center machinery-Plan---24x36
E4.--Brection diagram of center mach. Longt«<. & Trans.
sections 24x36

E5---Erection diagram End ani Center Wedges & End Latch

~ == 24x36

E6---EFrection diagram for shafting and operator's house

~-=24x36
Sheet 1---Top chord section U1-U3- - - - - 24x36
2---End Posts EPl - - - - - - 24x36
3---End Posts EP2 - - - - - - 24x36
4e--Portals and Sway bracing SBl-2-3-4 - - 24x36
5---Posts and diagonals U 2L2<U 3L3-U4L4-L2U1-L2U 3-L3U4-
L4uU5 - - - - - - - - - 24x36
6---Top Chords U3-U5 - - - 7. - - 24x36

Je--Stringers and Luterals (Top) TL1-2-3-4, $1-2-3-4-5-6-7-
‘=> en

 
10-S4-8-9 - - - - -

G---Floor beams-End and Intermediate FB1-2-3

9---Bottom chord sections L2-L4 -

10---Center Posts and Sway Bracing SB5-6-

U6-L6 - - - - - .

ll---Bottom chord sections LO-L2 -

-8-9-

l2---Hangers, Stringers, & Bottom Laterals SLl-

Ll-13 incl., UlL1, U5SL5, Rl-2-4— -
l3---Machinery supports MS3-4-5-6-9

14---Mac.inery sunports MS1-2-7-5-12

15---Track az:d Pinions Girders T1-G4-P3

16---Center cross Girder G5 - -
17---Hand Railing HR1-2-3-4-5-6 -

18---Hani Railing HR7-8-9 -

19---Center Gussets an“? Brackets CGl, BKl-2

20---Str:ngers and Girders §11-290 incl. and Gi

21---Floor beans and Girders FB4-5, G2, MS10-11

22e--Botton cnord L4L6 - - -

10,

24x 36
24x 36

24x 36

'
n
m4

Ly
On

§ 8 8 8 8 8 8 58

ree ee eee
~~ A ee RS KH KH BH
WwW Ww Ww Ww WY we Be wD
oO W@W Ad dw AQ @®Q a

6
>
”

lw
On

- 24x36

23---Balance Wieel Girder and Machinery supports G3,

MS13-19 incl., P5-6 - - -

C9214-Cl---Collar M20 ana Plate wasner N27

C9213-Cl---Pins & Recessed Nuts U5 & U6, PH29

C9213-C2---Rye Bars U5-U6 and Counters (none)

C9213-C3---Anchor bolts swedged and wedged 116

C9213-C4---Anchor bolts - - -

C9213-c5---Ring Fills RFl-2 - -

C9213-c6---Field Rivets and volts

C9213-c7---Field Rivets and bolts

- 24x36

- 12x16

12x16

12x16

- 12x14
- 12x16

12x16

12x16

12x16
3.

Ml---Center an¢d End wedres Cl-C2-C3 - - - - 12x30
M2---End Latch M2 and Counter weirht bars M3 - - 12x30
M3---Wor.is and worm wneels F1l-F2-C6 - - - «+ 12x30

M4=2--Oilbox C4 and center base C5 Eyeb:lts FD - 12x30

M5---Discs F3, 4, C7? nd uyper center casting Cl0- 12x30
M6---Worm wheel bearings C8, Cll and cap C9 =~ = 12x30
M7---Connecting Rods FO6-F§8 and Levers CB-Cl2 for end

and center Lift - - - - - - - 12x30
MS---Bearings for Center and End Wedge Machinery
Bl-2-3-4- - - ". - - -  » -12x 30
M9---Connecting Rods F-7-9-10-11 - - - ~12x30

M10---Details cf Base & Girder Center Werge base

C16 and guide C17 -= - - - - - - 12x30
Mll---Levers and Bearings C14-15-18-19 and B5-8 ~12x30
Ml2--eBeurings and couplings C2Q-23 incl. = - -12x30
M13---End wedge and Latch shaftineg S1-5 incl. - -12x30

N14---Center en? wedce & Latch, Pins and Rollers N3-
4-5-, 57-68-20 - - - - - - ~12x30
M15+--Pins an* Collars M6-7-9-10-11-12-22 - - 12x30

M16---Couplings ind Bearings for line shaft C42-43,

C24-25-26 - - - “ ~ ~ ~12x30
M17---Shafts S9-13 incl. - - - - ~12x30
Mlf&---Rack and Pinion at Center C27-C28 - -~12x30
Ml9---Union bearing BY - - - - - 12x30
M20---Bearings for Ce:.ter Machinery B10-12-13 -12x 30
M21---Union bearings Bll - - - - -12x30
M22---Gears at center C29-30-31 - - -12x30
M23---Gears at Center C32-33-34-3¢6-39 - -12x30

- -12x30

M24---Shafts at center $14-15-16-17
4.

M29s--Balarnce wheels and beerings C35-36-37 - - 12x30
M26---Shafts §18-19-21-22-23 - - - - 12x 30
M27---Phosphor-btronze waners MB-1@ inch - - 12x30
M28---Shime  - - - - . - - 12x30
M29---Shims - - - - - - - 12x 30
M30-- Grease cups and oil cups - - - 12x30
M31l---Turned tolts - - - - - 12x30
M32---Cears and bearings (40-41, B14-15-16-8 “ 12x 30
M23---Brake wheel & capstan C44-45, M14 - - 12x30
M34---Rods and Levers - - - - - 12x30
M35---Handles, Knuckles, end Cotters - - 12x30
M36---Shaft couplings & levers (brakes) - - 12x30
M37---Snims~ - - - - - - - 12x30
M38---Turned bolts - - - - - - 12x30

M1lOl---Name plates - - - - - - 12x30
OUTLINE
ANALYSIS OF DRAWBRIDGE.

1. Estimate dead weight of all structural steel.

<. Bstimate value of top and bottom dead panel concentrations.

3. Diagram and tabulate dead load cantilever stresses.

4, Calculate left reaction for dead load continuous and cal-
culate and tabulate stresses due to the uplift of 1000# at each
end.

5. Combine stresses dead load cantilever and uplift of re-
action for dead load continuous and tabulate as dead load contin-
uous.

6. Calculate values of left reaction for live panel load of
1000# at each panel of bridge and plot influence line for Ro.

7+ Calculate ordinates for sll chord stresses. Live load
continuous.

8. Calculate ordinates for all web stresses. Live load con-
tinuous.

9. Plot influence lines for all chord and web si:esses. Live
load continuous.

19. Using live panel loads calculate and tabulate maximum pose
itive and negative live load continuous chord stresses.

ll. Using live panel loads calculate and tabulate maximum pos-
itive and negative live lcad continuous chord stresses.

12. Calculate and tabulate maximum, positive or negative chord
Stresses, live load simple span.

13. Calculate and tabulate maximum, positive and negative web
Stresses, live load simple span.

14. Calculate maximum uplift on left reaction. Live load ccne-

tinuous,
656

15. Calculate and tabulate the len;ths and areas of all main
members, and the unit stresses an? changes in len¢eth of all num-
bers under action of a l# load at center pier with pier removed.

16. Draw Williot diagram for above loading.

17. Compute true left reacticns for 1-00# panel loads at each
panel point of span and note corr-ecticn to approximate continuous
beam method.

18. Correct dead and live load continuous s.resses for the
above correcticn ir left reaction.

19. Tabulate the maximum combined stresses in all numbers note
ing the case and panel points loaded with live load to produce
same. Include in this table the actual unit stresses produced by
above maximum stresses and the units allowed by specificaticn to-
gether with the % by which the actual exceeds the allowed when such

case occurs.
ts

INTRODUCTION

In July 1915 the American Bridge Co. built two highway
bridges, very similar in character, which were erected in Cali-
fornia. They were both draw-bridges of the center pin bearing
type and were built from the same set of plans. With the exceptign
of the two center panels, both were of the parallel chord type con-
taining nine panels each and were of 257'-0" span center to center
of end bearings.

The clear road way was 21'-0" and was paved with creosoted
wood blocks resting on a double plank flooring.

Both bridges were provided with end wedfes and center wedges
to eliminate the pounding caused by the passage of trains and to
care for the variable deflections of the free ends of the truss
also end latchs to guide the structure to a proper alignment. The
bridges were arranged so that they could be operated either vy
power or by hand and the design of the machinery and machinery sup-
ports was included in the plans.

To use the American Bridge Co.'s designation for these bridges
contract No. C9213 was built over Old River between San Joaquin and
Contra Costa counties, Claifornia, while No. C9216 was built over
Middle River in San Joaquin county, California.

Since these bridges were different only in some of the detxuils
the analysis of one was sufficient to cover toth. So No. C9213
was chosen to analyze.

From the plans which were obtainable it was impossicle to find
the specifications or loading used in the original design; so it
was decided to use standard specifications (Milo Ketchum's speci-

fications for highway bridges and his class B loading which are
commo ily used vecause the floor system of this oridge is not
materially different from triat of a simple span bridge, the floor

system was omitted and the main truss memvers only were reviewed.
 

DISCUSSION

The bridge was analyzed for four conditions of loading,

1. Dead Load Cantilever, 2. Dead Load Continuous, 3. Live Load
Continuous, and 4. Live Load Simple Span.

Plate 1 is a marker diagran of the truss, and from it an idea
may be had of the general form of the truss an-:].zed.

Wnen the tLridge is swinging from the center pier, or when the
end wedges are loose, or just touching without prodicing an uplift
the truss members get a stress from the cantilever effect. The
stresses s:re determined graphically by placing the true dead
weight panel concentrations on the respective panel points and
solving for the stress in the members by a stress diagram as shown
on P2. These stresses were then scaled from the dingram and tab-
ulate ?, on P2 also.

When as is usually the case the end wedges are driven tight
enough to bring the bridge to a bearing at three points the bridge
acts somewhat as a continuous beam, and dead load continuous
stress;:s are produced. The end wedges however must be driven just
tisht enoug: to take out the deflection of the span when swinging.

Dead load continuous stress’s may be considered to be made
up of two parts, namely those produced by the weight of the bridge
Supported at the center, and those produced by the wedge uplift
at the ends, and considered as anchored at the center pier. Since
the stresses jue to the weicnt of the bridge supported at the
center, or dead load cantilevzr have already been considered, it
only remains to find those due to the uplift of the reactions and
combine with the cantilever to fet the dead loud continuous

stresses. The stresses due to a 1000# uplift at the left reaction
 

 

LQ.

were found by a graphical solution, P3, and these stresses were
multiplied by the summationa of the reactions due to the separate
panel loads, found by the continuous beam theory. The final
stresses obtained by ti: is m:thod were combined with the dead load
cantilever stresses to fcrm the dead load continuous stresses.

The live load continous stresses were calculated by the
continuous beam theory first and corrected later by means of true
reactions found by means of a Williot Diagram in connection with
the theory of rigidity. The conti::uous beam theory consists of
calculating the reaction at the right and left supports, produced
by a 1000# load at each panel point successively. The stress
produced in each member vy each separate reaction is then cale
culated and the positive and negative results summed up giving a
positive and negative force respectively in each member. As an
aid in checking the accuracy of this work typical influence lines
were drawn for the members of the truss and are shown in P6 & P7.
The influence lines were not used in solving for stresses, the
work being entirely analytical.

The negative reactions or those produced at the left support
by panel loads on the right half of the span were calculated by
means of the formula Ro e “E (K-K3) in which Ro equals the neg-
ative reaction, P equals the pane] load ef one pig (1000#) and
K is the ratio of the distance of the panel point in question to
the right support, to the length of the half span. In like man-
ner the formular for positive reactions at the left support R, =
$= (4-5K plus K3) was used.

If the end and center wedges are driven just tight enough to

make a food fit without producing an uplift at the supports, and
ll.

a train comes on the brid;,e, the loaded half of tue bride cts as
a Bimple epan for live loail andlive lozi simile s:an stresses are
produced. He chord stresses were computed aialytically .y means
of the method of chori incruments, with each panel point loai equal
to 49,000f. The web members were calculated by the method of maxi-
mum shears. both positive and negative stresses were cum uted for
each iemser and tabulated for euch me.iber under live load simple
span. (Care 1V, T40). To these stresses impact was aided calcue-
lated from Spec. 29, FP. 141, S. H. 5 .

When a brid, e is built the weigtit of the bridve itself and
the live load wiich cozes on Lt cnuses tue dbrid.e to sar or deflect
from the horizontal. To provide for this deflection when designiny
the bridze the amount and direction of movement of eich member must
be known. This i@ ietermined by weans of the Williot Deformation

Diagram. To construct this diagram it is first necessary to know
the change in length of each member jue to -the loading for which
the deflections are wanted. This change in length is comruted
from the formula I z si in which I equals the chan.e in
length, s equals the unit etress, 1 equals the len:th of the meme
oer, and E equals the modulus of elasticity.

Knowing the change in length of all members the dillinrd
Ningram is constructed as explained in part 2=--Rodfs and Brides,
vy tserriman ani Jacoby. In order to find the deflection of the
ends of the truss 80 as to determine the amount of wedve movement
to provide for, it is necessary to iIraw a Williot Diagram for dead
load cantilever. The changes in length for this condition are
Given in T45.

Since the trusses are no. of a constant desth thrutout and

the sectionil arrcras of tiie members are variable, the moment of
 

 

deai load cantilever to form deai load continuous.

The true live load continuous stresses were found by means of
the Wiiliot Diagram ani the Theorem of Rigidity. The stresses in
the members perviously found, by placing a 1000# load at each
panel point in succession, wor tue continuous oeam theory, stresses
were multiplied by the ratio of the Theorem of Rigidity reaction
to its corresponding Continuous wean Theory reaction, viving the
true stresses in the members. This was done simply to save the
time which would have to have veen spent in calcul .ting the
stresscs from the true reuictions in tiie usuril manner. hese
stresses were multiplied vo, the 49 kip panel loau to produce the
total true live loai continuous stresses. The impact was obtaine
ed by the formula I = AO 300 = 18%. (speo. 36 page 141 S. H.
Be) The impact was added to the live loai stresses to make the
total live loai continuous stresses.

VYhen a bridge is designed it must be made to stand the max-
imum possible stress that can ever occur in the members, due to
an assumed liberal loading to provide for future increase. To
get this mazimum stress for : given member all the possible practe
icable combinations of stresses were mi.e and the liar est positive
and largest negative stress produced, by tiese combinations were
“abulated. The combinations ‘pussivle to make are Case 1 dead load
cantilever, Case 1 and 1V dead load cantilever and live load sim-
ple s,an, Case 1 and 111 deai load cantilever and live load contine
uous, Case 11 and 111 dead loai continuo s and live load continuous

" Wuen the max positive and mix negative stresses were taoulated
the actual unit stresses were Calculated. In the case of pure tene-
Bion and compression the total stress was divided by the cross

sectional area to get the unit stress. In the case of alternating

 

 

 

 

 
13.

inertia of the whole section is not constant. Hence the Contin-
uous Beam Tneory previously used in finding the live and dead
load erid reactions w.s in error. To find the true value of the
reactions proceed as follows : By the Theorem of Rigidity the
center reaction for a load at any panel point is equal to the load
times the ratio between the deflection at the given panel point
and the deflection at the center, due to the same load placed at
the center with the center peir removed. See Modern “ramed
Structures Vol. 11. Johnson, Bryan, and Turneaure. A Williot
Diagram was constructed to ortain the Jeflections due to a l#
load at the center with the center pier removed. The deflections
were scaled from this diagram and the center reuictions calculated
for a 10CO# load at each panel point. The left reactions were

then calculated by the formula Ry «# 500 (1 plus K) -Ry in which K

is the ratio of the distance of the panel point in question from
the center of the truss to the length of the half span, and R, is
the center reaction just ottained. Since the sum of the three
reactions must equal zero in each case, the righ. reactions Ryo were
found by assigning to them such values that this result was obtain-
ed.

The next step in the analysis was to correct the live and
dead load continuous stresses for the true reactions found. This
was easily cone in the case of the dead load continuous stresses
by multiplying the reaction produced by the 1 Kip load as obtained
above by the actual dead panel load giving the total reaction in
each case. The algebraic summation of these guve the true left
reaction. The stresses obtained by a 1000# uplift were multiplied

by this reaction and the resulting stresses were combine? wit?
 
stresses, however, where the stress cnanges from tension to couprese”
ion, or vica vers: during the passi.e cf the live load th s;:ece
fications Tor design say that the member must ve design: : for the
larger max stress plus one half the cross sectional area required

for the max ctress of opposite sign. To find thea actual upit stress
in this case, the following formula were ievised by Frofessor

m@lick. When the positive max stress was tue larger 5,#T plus S

a.

A

When the nc gative stress was the larger S, * &@ C plus iT. K. Where
2A
S_, equals the unit tensile str:ss, Sg equals the unit compressor

stress, T equals the max total p.sitive stress, C equals the mix
total ne,ative stress, A equa ls the cross sectional area of the
member, and K equals = allowed vy the specifications. The allowe-
ed unit stresses were computed for the compressive stresses by the
formula S = 16,000=70 1 where S equals the allowed unit «stress, r
equals the least radiue of gyration, and 1 equals the lenz,th of
the memver. Wherever the actual unit stress ws larger than the
allowed, tiie per cent of excess was tabulated.

It was found in the analysis that the chord memvers were
quite badly overestressed, while the web members wre almost all
on the safe side. This might ve ex laiied oy the fict th:t the
loading and specifications uscd in the design were unknown. Ive
idently they were not the specifications to use, or else there
was some bad blunder in the design, or the results would check
more closely with those which were obtained in the analysis, with

specifications in common use.
 

 

 

 

 

 

 

 

 

 

 

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