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Design and Construction of a

Model Railroad Bridge

A Thesis Submitted to
the Faculty of
MICHIGAN STATE COLLEGE
of
AGRICULTURE AND APPLIED SCIENCE

BY

\_,
\i.

LL 3'. [list 0; D. Harrington

Candidates for the Degree of

Bachelor of Science

June 1932

‘ THESIS

FOREWORD

During the winter of 1952, the authors visited the
National Road Builders Association's exhibit of various
road surfaces and road maintenance equipment at Detroit,
Michigan. There we saw a miniature Pratt truss railroad
bridge exhibited by the Ohio State Highway Department.
There was an electric locomotive repeatedly crossing the
bridge and the changes of stress in the various members was
registered on small dials attached to them.

At the suggestion of Prof. Allen and Mr. Rothgery
of this college, the authors decided to design and construct
a somewhat larger and more elaborate model for their thesis.

The details of the design and construction are as here-
inafter described. The model is presented with our compli-
ments to the Civil Engineering department of Michigan State
College with the hOpe that it may be of some assistance in

class instruction in bridge analysis and design.

104094

ACKNOWLEDGEMENT

The authors wish to thank Professor Allen and Mr. Roth-
gery for their suggestions, and also the Michigan Sheet Metal

Works for the use of their sh0p and equipment.

TABLE OF CONTENTS

Materials used in construction
Design and construction details
Dead load stresses

Live load stresses

Summary of stresses

Drawing of Joint connections
Drawing of gauge details

Photographs

Page

10
11
12

13

MATERIALS USED IN CONSTRUCTION

Lower chord members

Upper chord members
Verticals

End diagonal (compression)
Diagonals (tension)

Floor beams

Stringers

Track

Gauge springs

Gauge pointers

Gauge dials

1"
1"

1n
'é'

1"

x

X

X

I

14 ga. band iron
14 ga. band iron
14 ga. band iron

14 ga. band iron

3/16" round rods

}' round rods

%" I beams, formed from IX tin
00 gauge toy train track
9/16" x 24 ga. spring brass

1/8" copper rods

IX tin

DESIGN AND CONSTRUCTION

The type of truss chosen was a Pratt truss with tension
diagonals, counters being placed in the center panels to take
the reversal of stress caused by the live loading.

As a larger bridge than that shown at the Road Show was
desired, it was decided to use a light gauge band iron of
varying widths depending upon the member under construction.

As far as possible, we made the members of sizes similar
to those of a large bridge; however, this was impossible in
our case on account of the method used in joint construction.
The many members terminating in‘a lower chord joint near the
center of the bridge necessitated a width of about one inch
for the lower chord members. By reference to the sketches on
page 11, the details just described will be made more clear.

The panels were made 10' center to center - the height
12" center to center. This gave a diagonal distance of 15.62"
center to center. The trusses were placed 8' on centers, with
the stringers 5%” apart.

The solid truss was constructed first, and the details
of the joint connections decided upon as construction pro-
gressed. This was found to be the most practical way as
difficulties arose during construction which could not be
provided for in the design.

We made three jigs for the members; one each for the
chords, verticals, and diagonals. This insured that all

similar members would be the same length when finished.

These jigs consisted of a flat strip of 1" band iron on which
were welded two upright &" rods exactly 10, 12, or 15.62
inches apart center to center. Each member was constructed
and assembled on its respective jig. This gave us a uniform
fit and bearing of all members.

A typical chord member consisted of a strip of the 1"
band iron about 9%" long, with a set of clips thru which the
ends of the floor beams passed soldered to each end. See
details on page 11.

The verticals were made in a similar manner. The tension
diagonals had a thin strip of sheet metal with a slotted hole
in one end, fasted to each end of the diagonal. This was done
to ensure that the diagonals would take no compression.

The floor beams consisted of &" rods 11" long, threaded
at each end for a distance of about %". Washers were soldered
1%" from each end so that the trusses would be 7" apart in the
clear. The members of each truss were slipped on from the
outside toward the center, and then held in place by means of
a washer and nut at each panel point.

The stringers were made by forming two %"

channels,
placing them back to back, and soldering. The stringers were
designed so that they were free to pivot on the floor beams.
This was effected by slotting the end of one stringer and
soldering two rods }" apart on the end of the next stringer.

Sidewise movement was prevented by soldering narrow clips

on to the floor beams next to the rods.

The track used was of the wide gauge used for toy trains.
The sections were not of the prOper length, however, and had
to be cut off to size. The track as purchased had three rails.
This center rail was removed from each section and used in the
construction of additional sections. This called for additional
ties which were formed out of IX tin. The ties were soldered
directly to the stringers. There was a small space left at
each panel point to allow the floor beam to deflect without
causing any binding of the track or stringer.

The springs used in the split members were made by form-
ing semicircular loops of the strips of spring brass. Two of
these sections were bolted back to back at each split to pre-
vent the members from buckling under compression.

The pointer of each gauge was pivoted at the end of a
narrow strip of metal which was bolted to one part of the
member and projected out into the middle of the circular loop.
From the other part of the member a flat notched strip engaged
the pointer near the pivot. By the principle of the lever,
the movement in the springs was greatly magnified out at the
end of the pointer. For a more complete description of these
gauges, see details on page 12.

After final assembly, the bridge was weighed and the dead

stresses computed as described on the following pages:

DEAD LOAD STRESSES IN TRUSS MEMBERS

 

 

'-l-—-IZ—q

 

 

 

 

p

 

 

 

e @ I0" = 5-0"
Dead load of bridge equals 18#
Dead load per truss equals‘ 9#
Dead load per panel equals 9/6, or 1.5# per panel
Distribution of dead load: 2
Upper chord takes 1/3 of 1.5#, or 0.5# per panel
Lower chord takes 2/5 of 1.5#, or 1.0# per panel

4* it II:
as ' c5 06

 

 

Dead Stress Diagram:

 

 

 

 

 

Sample Computations:

The stresses were computed by the index stress method,
the index of stress in a diagonal being the vertical component
of stress therein. In order to obtain the true stresses, the
individual index stress must be multiplied by the ratio of
bar length to vertical projection for the diagonals, by the
ratio of panel length to truss depth for the chords.

Dead Stress Computations (cont):

With the panel loads written on the diagram, the stresses
were written by inspection as follows: Starting with joint
US, the stress in the center vertical is -O.5# (minus indi-
cating compression). At joint L5 the tensile vertical com-
ponent in each diagonal equals one-half the sum of vertical
stress and panel load, this joint being at the center of the
span. This gives a V component of stress in diagonal U2-L5
as (1.0 plus 0.5) / 2, or plus O.75#.. At joint U2 there is
a downward load of 0.5 and a downward vertical component in
the diagonal of 0.75 to be balanced by the compression in the
vertical U2-L2, or this compression is equal to their sum, or
-1.25#. Thus the work proceeded to joints L2, U1 etc. in
turn, a check being afforded at LG by an independent compu-
tation of the reactions. Next the horizontal components of
the diagonals were written down and then the chord stresses,
proceeding joint by joint toward the center, first on one
chord, then on the other.

The first check for the chord stresses was the require-
ment of equal stress in bars diagonally Opposite as Ul-U2
and.L2-L5. The second and positive verification was the in-
dependent computation of the stress in the top chord at the
center, which equals the bending moment at the center of the
span divided'by the truss depth. After this check, the actual

stresses in the diagonals were added to the diagram.

We experimented with live loads of different weights
until a load was found which was heavy enough to cause a re-
versal of stress which would be taken by the counters in the
middle panels. A special car was designed to carry this
weight across the bridge. The weight selected was a piece of
steel shafting 3' in diameter and 10" long which weighed 20#.

The maximum swing of each pointer was marked on each
gauge and this point marked with the maximum live stress as
computed on the following pages:

After final adjustments were made using the live load
selected, the bridge was sprayed with aluminum paint, the
gauges calibrated as above described, and the completed model
presented to the Civil Engineering department of the Michigan
State College.

LIVE LOAD STRESSES IN TRUSS MEMBERS

Live Load Data:

 

Live load consists of a single 20# weight.

Therefore the weight per truss is 10#

Sample Computations:

 

To determine the position of the load for the maximum
stress in each bar required the drawing of an influence line
for stress in that bar.

While in this particular method of loading, the effect
of a concentrated load is not obtained, yet as this is only
a relative measure of stress, the maximum stresses were com-
puted on the basis of a 10# concentrated weight.

Following are the computations for maximum live stress
in one each of the different types of members:

CHORD MEMBER Ul-U2

Maximum stress occurs with the load at panel point 2.

7////?>// '/ 7 ’

Sum M about L2:

 

(2/3 x 10) x 20 = 12 s
12 s = 400/56
8 a 11.1}? Comp.

 

 

VERTICAL MEMBER Ul-Ll

Maximum stress occurs with the load at panel point 1.

My

Taking the joint L1, and Sum V equals 0:

._.A

S - 10 I 0

S=W

DIAGONAL MEMBER U1-L2

Maximum Stress occurs with the load at panel point 2.

Left Reaction vL = 4/6 x 10:=40/6

“1----j2
Sum V equals 0:
v - 40/6 = 0
V =340/6
S I 40/6 x 15.62/12
8 = 8.75# Tension

 

SUMMARV OF STRESSES

 

Member Dead Stress Position of Maximum
Load for Max. Live Stress
Ul-U2 5.00# 0 Panel pt. 2 11.11# c
U2-U5 5.65# c " " 5 12.50# c
LO-Ll 6.16# T " " 1 6.95# T
Ll-L2 5.15# T " " 1 6.95# T
L2-L5 : 5.00# T " " 2 8.64# T
Ul-Ll 1.00# T " " 1_ 10.00# T
U2-L2 1.25# c " " 3 5.00# c
U5-L5 0.50# c " “ 2 5.33# G
Ul-LO 4.89# c " " 1 10.85# c
U1-L2 2.96# T " " 2 8.75# T
U2-L5 0.98# T " " 3 6.50# T
U5-L2 0.00# " " 2 4.55# T

 

II

 

 

 

 

 

TYPICAL JOINT

 

L l r

I:

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j
Ec//,'o soldered f0 mem be r

TY PICAL CLIP CONNECTION

 

 

/Z

 

 

 

 

 

 

 

 

 

 

 

 

 

FEONT VIEW Of’ GAUGE. WITH DIAL
REMOVED

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6

TOP I/IhW OF GAUGE WITH DIAL
AND TOP SEMICIQCULAE SPRING
REMOVED

PHOTOGR APRS

 

PHOTOGRAPHS

 

 

FINIS

 

 

 

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