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THE (INVESTIGATION OF THE
TIMBER CONCRETE COMPOSITE
BRIDGE DECKS DESIGN

Thesis for flu chm of M. S.
MICHtGAN STATE COLLEGE
Yu Chi Lin
€949

THESIS

This is to certilg that the

thesis entitlml

THE IT‘IVECTIC..TION 0? Ti? TIL‘JIBET‘. C'TLIICLLTE
CO‘-'E”T!SITE 3‘": EDGE DFCKS DESIGN

presentml hi]

Yu Chi Lin

has been accepted towards fullillmcnt

0f the requirements for

M.S. degree in Civil Engr.

,. z ,/ x A ‘ .
/1" A [j’L/W‘v I’M"
V

Major l'vrnlcswr

Date JUlY 2;, 1949

0169

 

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THE IKVESTIGATION OF THE TIMBER CONCRETE

COMPOSITE BRIDGE DECKS ESIGN

BY

YU CHI LIN

“

A THESIS
Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Civil Engineering

July 19h?

TH 2815

A CKN OWLEDGNEI‘T S

1

The writer wishes to acknowledge his inflectedness
to Professor C. L. Allen and Professor C. A. Miller
for their untiring assistances and suggestions in the
prepa ation of the manuscript. Appreciation is also

extended to Professor C. h. Cade for his encoura;e-

ment and valuable suSLestions.

218488

w‘...

Introduction

Contents

General Treatment of the Design

a. Timber Base
0. Shear-Developers and Uplift Spikes

0. Concrete Hat

Ekperimental Treatment of the Design

a. Comparison
b. Comparison
c. Comparison
d. Comparison
e. Effects of

of Ultimate Strength

of Different Types of Shear Connections
of Deflection

of End Slip

Alternated Loads

f. Location of Neutral Axis

. Temperature Effect

Evolution of Theory

he Practical Design

Introduction

The purpose of this investigation of the tlnber-concrete
composite design is to take advantages in the locations where
he timber is at low cost and the cement is rather easy to
obtain. In other words, this investigation aimed specifically
at a low cost construction with a comparatively long service.

The timber-concrete composite construction presented
herein is aimed at reducing construction costs, through
primarily reduction of the steel cost and secondly of on-the-
job labor.

‘

In til

3 connection, some of the features by which this

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design will accomplish construction at lower costs are pre—
sented in the following:

1.

+3

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I.

he strength properties 0 the concrete wearing

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urface in combination with the timber has been
utilized to support the load.

2. Ther is no need for falsework or form-work

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1. Details are such that the most available grades
and sizes of lumber may be used; this is the most
economical way to buy lumber.

h. Steel or hardware is held to a minimum.

5. Span length is variable, permitting a selection

for an economic balance between deck and sub-

structure
..

6. Loading and roadway WIMVH «av be selected to suit

cl

local conditions.

F; ‘ ’ o .‘1 1,‘ , A“ ,0 m _ W1 '_ ..
1. Panel units oi ,ne lhnnnntUd \.
“.0 - - - ‘1“ .
fab'icated and as eduIEd.

Labor costs at present constitute nearlv 69 oer cent of

U A.

0
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the total cost against {3 per cent for materia s. A reduction

n labor costs of one-third would thus eliect a saving of 20
to

pen cent of total cost not to mention the reducin; costs Oi

inaterials.

General Treahncdt of the Composite Timber-Concrete
C‘- on s tru c tin n.

”i timber-concrete composite construction can be briefly

oescriwec as a laminated wood slab of treated plank rig

interlocked with a heavy concrete mat. This assembly is trans-

formed into a unit adequate for bridge decks desi

81’1le f0]? any
standard highway loading, or for piers, docks, warehouse, reaps
or other siructures requiring heavy duty floor.

The wood slab or tiaber vase is usually of 2 incn
g to 12 inches in width, depending on Span and load.
"1“ -

lne ultcrnate plank are of different width, so to have a raise

07 1-3/8 inch to 2 inches to fore the longitudinal nrooves.

K.)

*"5

The same e feet may be obtained by usintr ;,>l:.-.:..:1{ of two Widths

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and alternating them in the assembly. Small trapezoidal steel

02

plate —shear—develop~rs are driven into pre-cut transverse slots

in these grooves, forminv the shear connection between wood and

K.)

-‘

concrete. Uplift spikes or dowels are driven into the raised
laminations on from 2 to h foot centers to restrain the ten-
dency of concrete to curl. These are not taken into account
in computing Shear reinforcement, but d: add to it.

The principal problem in the design of slabs, of whatever

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to lateral distribution of a o>n-

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:riture,
centratcd load. Obviously, one must know what load is to be
carried on the particular width of slab used as the unit on

which the calculations are based. The elements that enter into

the problem are numerous and difficult to evaluate, so depend-

ence has been put very larv empirical formulas.

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Laminated wood pieces sviked to :ther in accor:

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a given pattern and securely bonded to a concrgte mat function
effectively in carrying transverse stresses. Where large

scale installations are involved it will be advantageous to

employ prefabricated panels of uniform Wlfitls nine u1 of wood

J.

laminations ri idly fastened together with soiral dowels and

accurately bored for driving of additional dowels in the field,
to join the separate panels in one whole slab assembly, The
dowels are effectively bonded in the wood because their

9 W

Spirally grooved ridges lie outSice the diameter of the lead
hole in which the dowel is entered. Consequently, they provide
effective transverse reinforcement for the composite slab.

For ordinarily, the span lengths used in trestle con-
struction all plank should be full panel length, laid immediate—
ly on the support in a direction parallel to the roadway center
line. Where in multiple span construction, a continuous, un-
broken deck is often desirable, one-third of the laminations

are butt'jointed over the support centers and one-third at or

bein

0')

near each quarter-Span point, the joint made in regular

rotation. The theory back of this is no matter what kind of
arrangements are possible, it is necessary that at least two-

ioints.

thirds of the strips should be continuous across Splice d

In the above arrangement there are two-thirds of the strips
extend across and are effective at any of these points, and a

full timbe section extends throughout the midspan reach be-

tween quarter points.

Shear DevelOpers and Uplift Spikes.
The shear develOpers are made of steel plate in trapesoidal

shapes. The standard dimensions are 3-3/h.in. on the top and

1/2 in. at the bottom. A 3”

eight or altitude of 3-1/2 Wig/W/Z/V
4 /
at

 

D“

in. with a thickness of 3/32

     
    

in. They are driven in the

 

pre-cut slots of the timber
base, their tops protrude
1/2 in. above the timber so
as to engage the concrete mat.
The Spacing of the shear develOpers is froa the plans and should
be followed accurately. However, a slight shifts in Spacing
to avoid any knots in the timber which would prevent their
effective seating.

The uplift Spikes are also driven into the raised timber
and their protruding heads

are embedded well in the

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250' 2‘0” 2'0 230”_L_ Z-o’:
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flu"

,1 5 0/5””

 

concrete mat to preclude

 

 

 

 

 

 

any tendency to vertical ”gag/$97155 F.

 

 

separation between the

 

concrete and the timber
due to their curling
action of concrete induced by differential tenperatures on its

top and bottom surfaces.

-5-

Cormnfietezifet.

_ . 1- . -- -- -H in .._-. ‘e,.-A..._,1 J.‘
isle nilflnf'i’ftw} to HG: poured. Lu‘l by DJ. Law} jéuilllie.l+‘-l- I-lif-

oer base form a met over the base and is only reinforced

for shrinkage and temperature stresses to prevent cracking.
Generally the mat reinforcement consists of a mesh made up

of 3/8-in. or l/Z-in. round bars placed from Q to 12 inches

I

on centers both longitudinally and transverseIV. However,

n continuous s

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pans, where ne“ative moment occurs over the

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suflports, su' icient steel is added to take care of the

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stresses celculeted. Tor reinforcing these stresses generally
the bars of about half Span length are staggered between the
longitudinal he‘s. In case the longitudinal bars should

call for Splicine thev are preferably to be spliced at mid-

syan and not over a supoort. The alternate bars should

extend across the

oints in the timber base near the quarter

points.

-7-

Experimental Treatment of the Composite

Timber-Concrete Construction.

Comparison of Ultimate Strength:-

It is essential, in the first place, to see if there is
any benefit resulting from the use of composite construction.
To start with we first compare the ultimate strength of the
composite beans with that of plain timber beams of correspond-
ing stem dimension. At once, we see that this is a fair com-
parison; for the reason that if the concrete deck were placed
upon the timber base without any connection between them, there
would be no increase in strength because of the deck. In fact,
if the timber base were removed from underneath the deck it
would not be able to withstand its own weith for an average
span of, say, 20 feet. From the above, we see, actually the
deck would be a burden on the timber base or strincers. However,
with prOper connection or adequate shear reinforcing, as tested
by Oregon State Highway Department as in this connection, it
shows that the strength of the composite bean is nearly double
that of the corrcSponding plain beams. Therefore it concludes
that "If a most suitable types of shears reinforcings were em-
ployed that the use of the composite type of construction will
produce structural members having an ultimate strength at least
twice that for the same materials and sizes used independently”.*

I

”Technical Bulletin No.1, Oregon State Highway Department,
pp. 71

-8-

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Comnosite

Tltlmate Strengths of

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4.

Comparison of

cams and Plain Beans

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These figures are taken from Tec

Note:

Oregon State Highway Department, pp. 72

-9-

Comparison of Ultimate Strength for

m*rw of Shear Connection Average for

Series Jo. l and No. 2

 

 

 

U/f/hd/e flay/i —- [Adfljl/Jdé 4/ 61/045

 

 

 

 

Jote: This figure is taken from Technical Bulletin No. 1,
Oregon Highway Department, pp. 73

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-10...

Comparison of the Different Types of Shear Connections.

Since the composite desi n is the combination in a

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structural member of two elements having different mechanical

properties, therefore, it requires a definite study about

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the behaviors of the horizontal and vertical snears as well

as the end slip at the junction of the two different elements
under different loadings including the alternated load. With
the aid of this study a better and more effective shear connec-
tions can be provided so as to produce the best results.

In this connection, I would like to quote.some the work

T

carried by Mr. B. h. Baldock and Er. C.B. McCullough of Oregon

State Highway Department on Loading Tests on a New Composite-

0 n

Type Short-span uwav Eridge Combining concrete and Timber

in Flexure.

The tests have een carried on by using two sizes of T-
beams. Series No. 1 includes all the beams of smaller size;
that is, those with 6" x 15" concrete flange and h" X 1h"

timber webs. Series Do. 2 iiéludes all of the beans of the

laraer size; tiat is, those with 6" x 2?

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concrete flange and
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6" X iU" timber web. all of tne tiMMEP used in tne webs or
stems of the beams graded somewhat under structural Douglas
fir the sticks beinv thus selected in order to re resent the
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lowest quality likely encountered under actual construction
conditions. All of the concrete was of Class D mix at defined
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in the Specifications for State Hi

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for the State of Orepon. Thii is a nominal 1:2:3 mix designed

t1 1:.» 2 8 do

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i&)'nimwluca2 corn retna M“LIC‘L¥‘J]]- Niiuasiwu.d rh)t .Lob.x I a ,
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pounds per sauere inch at "eye and is the class generally

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used by the Ore;en State Highway Department for brif e necas.

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_\/b‘ 1,~r)r'¢;;‘, Oi :‘wh‘fil' CQnIWOCt 93.11:) I 9t 6’. “96%, 8311‘]. 1-910 IDSdLII‘:
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earfii serdxms for>sw ch truue on

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sherxw connectuxnixvere 1%yate;.

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he first type of shear connection - t >e l — consisted

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O o- v O o , _ ‘ ‘ no _ ‘I “o _ p _ ,0 ‘1.“ ‘ o_ _
of B/U-lfl. bJ u-ln. round spikes, driven five incies into
the timber men. Holes slightly snnller than the Spikes were
bored before ihe 3 vi kes were driven In 0rd er to prevent

splitting of the tiuduer. The spikes were Spaced everv two

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”JOrts aflfl the load pOifltS gfld everv

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inCIWns beimmufifi tTw?:fil

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neiwx; getwneen tine lozul poixrts. Ehirttwnmnorer'the Endikems

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were StHSVGI“é-E(1 in three new so as to fu1'*thr-.>r 1“G«'1z":i(‘.€= the

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The timimr‘. alter the b

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tendency toward splitting 0

were driven, the tOp three inches eytended up a)ov; into
tile c<3ru3iwsize ‘wiieri i t 'WLIS IMDltfiééd. ELPKYUfld. tlien..

'Type 2 ccmniisted of dafméimi'the weed, 1mu4ether vdflfli the
orwed in them ty the concrete. Fetween the supports and
mints, the naps were five inches long With five
.des between the daps. between the load points, the da
were six inches long with twelve inches clear hettcen dups.

Type 3 was BVCCWWfiflNWtiOH of Type 1 Efllirere 2 with Slight

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N . . -— . - V- -c O . V ,. .. , ‘, a A , v . ‘
moUL icaticn. The Spaning cf the da)s was the same as Type
lNit time S’djmes vunre sqwieed Ave irw eacli<1wp, ()n twat menialaps

between the snpports and the loan points, and nune between

-12-
the load points. The daps were sawed out, and the Spikes were
placed before the timber was set up for pouring the concrete.

Type h made use of pipes in place of spikes and in much
the same manner as the Spikes in Type)» Two and one-half-
inch pipes (outside diameter), four anl one-half inches long,
were driven two and one-half inches into the timber and allowed
to extend up into the concrete flange a distance of two inches.
The pipes were Spaced at six and one—half-inch centers between
the supports and the load points and twelve and one-fourth-
inch centers between the load points. Holes one-sixteenth
inch smaller than the pipe diameter were bored before the
pipes were driven.

Type 5 consisted of h” X 3/h” x h" steel plates driven
into slots in the timber one inch deep and allowed to extend
three inches into the concrete. They were Spaced eight and
one-half inches apart between the supports and the load points
and fourteen inches between the load points.

From the above arrangement of shear connections, the re-
sults were summing up by Mr. Baldock and Mr. McCullough as
follows:

"First, the plain dap type of connection is wholly in-
adquate to develop the strength of the rest of the beam and
should not be used.

Second, slots and plates form a good connection from the
standpoint of rigidly, but for the sizes used in these tests,

permit the web to fail at low loads by horizontal shear be-

-13-

low the bottom of the plates. Since it is not feasible to
extend the plates far enoUgh into the timber stem to rein-
force it against this type of failure, the slots and plates
do not appear to be a suitable type of connection.

Third, the plain spikes form a fairly satisfactory method
of reinforcing, but they permit an excessive amount of end
slip and, consequently, too much deflection and too much inde-
pendent action, thereby reducing the strength of the beam.

This leaves (1) the pipes and (2) the combined Spikes
and daps as the most effective types with little room for
choice between them. However, there is still one factor influenc—
ing the selection which has not yet been considered; namely,
that the combined spikes and daps are somewhat cheaper than the
pipes, eSpecially in cases where the connection must be ex-
tended well into the web to reinforce it against horizontal
shearing stress. All in all, therefore, he combined spike and
dap connection - Type 3 - should be accorded first place with

Type h—pipes - a close second".

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Comparison of Deflection.

The matter of deflection will now be considered. It ap-
peared in the above that the use of a rigid connection between
deck and timber base would add considerably to the stiffness of
structures of this type. At a glance of the following tables
will suffice to draw the conclusion that the deflection of a
suitable-connected composite beam under a given loading will not

«H

be more than a; per cent of the corresponding deflection for

he same sizes and materials used independently.

‘71

Comparison of Ueflections for wach ?air of Pawns

Types of Shear Connection

Load Plain Plain Spikes Pipes Slots & Pla‘n Theo-
Spikes Daps & Daps Plates Beams retical

3

Series No. 1

5,000 0.07 0.06 0.05 0.06 0.05 0.26 ----
10,000 0.15 0.13 0.11 0.12 0.11 0.5, 0.10
15,000 0.23 0.19 0.17 0.19 0.17 0.88 .....
20,000 0.32 0-2h. 0.24 0.26 0.23 1.10 0.21
25,000 0.h3 b.32 0.31 0.33 0.30 1.53 ----
30,000 0.55 ---- 0.37 0.h1 0.37 ---- 0.32
35,300 0.71 ---- Goth 0.h8 O-HB _-__ _-__
h0,000 ---- ---- 0.52 0.56 0.51 —-—— ' --—-

All deflections given in inches.

Note:
This table is taken from Technical Bulletin Po. 1,
Oregon State Highway Department, pp. 70

-15-

3

Comparison of Deflections for Hacn fair of Pcans

 

15

Types oi Shear Connection

Series No. 2
Load Plain Plain. Spikes Pipes Slots & Plain Theo-
Spikes Daps & Daps Plates Beams rectical
5,000 0.03 0-0h 0.03 0.05 0.02 0.02 -___
10,000 0.06 0.08 0.06 0.08 0.06 0.h1 0.06
15,000 0.08 0.13 0.10 0.11 0.10 0.55 ----
20,000 0.11 0.17 0.13 0.16 0.13 0.73 0.12
25,000 0.16 0.21 0.16 0.19 0.16 0,92 -_-_
30,000 0.20 0.25 0.20 0.22 0.20 1.16 0.18
35,000 0.25 7.30 0.25 0.28 0.2% ---_ -_-_
h0,000 0.30 0.3M 0.3‘ 2.3% 0.28 ---- -_--
h5,000 0.35 0.38 0.3M 0.37 0.32 -——- ———_
50,000 0.h1 0.h3 0.39 0.81 0.,6 ---- -__-
55,000 0.87 --—- 0.us 0.h5 0.80 ---- ----
60,000 0.53 ---- 0.h8 0.51 0.55 ---- -_-_
65,000 0.’2 ---- ---- 0.57 0.51 -_-- -_--
70,000 0.73 ---- ---- 0.62 0.57 ---— —————
All deflections given in inches.
Note:
This table is taken from Bulletin No.1, CreLon State
Highway Department, pp. Tb

The ctmrvanina
types of shear connections will be next considered.

Sults of the comparison as tested by Grew-or

partment

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-16-

Comparison of End Slips.

‘d slip

State Hi

1

or eacn different

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The re-

he following statement with taFles to show

the end slips for each type of shear connection:

 

Comparisdn f 5nd Sli s for Pei f Pei s
Types of Shear Connection
Lori Plain Pliin c ikes Pipes Slots &
Spikes Daps Daps Plates
(1 0 “T
Series 30.
, r-’
5,'_I\IO 1.6 9.)! 0.]. 2.3 DOS
r’ I /
10,00 3.1 15d: 0.9 3.0 7.9
r'" A A
”3,130 8.1. f0.9 2.? SQKQ) 11.8
20,000 18.6 2h.8 3.5 7.1 17.6
r" r’
25,000 ,,.M 29.3 5.9 8.8 21.2
— o r4
30,000 61.0 --—— ~.5 1L.p 31.9

All end slips

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H
H
O

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an 1:10.71,

 

The results of tH

S

2 shown

in the above tables,

least

and daps give the Si

twpes Show a much 5

v gaeunijern a.Q()n

probably due to the

fit in the lain

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A.

is camper

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nt o1 SL_*

dafns and

Comparison 0. 9nd Slips 1or .0c? rair of Prams
Ty es rf Shear Codnectinn
Load Plain Plain Spikes Pipes Slots &
Spikes Daps a Daps Plates
Senies To. 2
5:050 ‘“*‘ “.8 ---- 0,1 --_--
10,000 ——-- 9.3 -—-- 0.1 --—--
15,000 --—— 12.1 —--- 0.3 0.2
20,000 ---- 15.0 ——u— 1.1 0.2
25,000 ---- 17.8 ---- 1.9 0.2
30, 00 k.h 29.; ——-- 3.3 0.3
35,000 12.3 23.5 —-«- 6.0 0.3
h0,000 22.0 26.5 1.8 9.2 0.6
A5,000 30.8 32.0 u.6 12.0 1.3
50.1 0 hh.0 37-0. 1h.3 15.1 1.8
55,00u 56.8 -—-- 19.0 19.5 3.0
60,033 75.0 ---- ?5.9 2%.3 t.0
65,000 101.2 --—- ——-- 30.0 8.6
70,000 130.6 —-—— -—-— 36.2 12.5
All qui slips Qfinnwi in ttmnummndths of‘2u1.ideh.

.30 711'
lDUaan LuJES ;A). 1

l-I

138

that combined spikes

next. The other three
111 ifl1:r1 tile:5e LVN),
In ettin a ti ht

the slots and plates

and to the tendency to spring and bend in the case of the
plain Spikes. The same information for the beams in series so.
ots and plates gave the least anount of slip in this
test, with Silkfis and daps second, and pipes third. The plain
spikes tnfbi'well for'iflrafhyser loads, lnmt as scmn1:%3'fiais type

of connection starts to slip it wives rapidly. The plain daps

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1

slip at a fairly nizh rate from the start and continue on to

.n
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il ure .

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It is obvious that the deflections of those beams and the
anount of end slip are closely related since the more positive

the shear connection the more nearly is comolete integral

ll be the deflection.

f—o

action attained, and, hence the less w
Effects of Alternated Loads

Witn the c omwio3 ite beam when te ested under the alternated
load, a certain aiaount of plastic disnlacenent in connection
with the end slip as it does in the static loading. However,
there is a partial elastic recovery. This plastic shear dis-
placement is undoubtedly the result of tightening up or seating

n

Of the shear connections accompanied by a local crushing o,

the timber fibers, or of the concrete, or of both. As has been

observed by the Oregon State hM ghway Department that as the
loading is alternately agplied and released, further succe e.sive
increments of plastic displacement become smaller as the number
of loal i cycles is in ncrea_se The total cumulative plastic

slippage approaches a fixed and definite value as the load

-19-
alternations are increased ind3finitely.
"Tests'to destruction of the beams subjected to the ap-

plication of alter atcd loads ind cated no appreciable loss

in ultimate strength as a result of such alternated loading.

Even the in:tial plastic displacements were of comparatively
small magnitude, and the additional plastic increments very

rapidly decreased to a nearly negligible value. In View of
these facts, there appears to be no danger of any material
alternation in the manner of stress distribution throughout

,he cross-section of a well-cesicned composite bean as a re-

P.
U

'e at the shear connection”.’

3,,
U

sult of slippa

Location of Neutral Axis.

If there were no connection between the concrete flange
and the timber stem and each section were perfectly free to
slip past the other, the top of the flange and the top of the
stem would be under compressive stress and the bottom of each

section would be under tensile stress with a neutral axis at

about thc_middle depth

0

f each section. On the other hand,
if the connection between the two sections could be made ab-
solutely tight and rigid with no Spring or slip of any kind,
entire integral action could be obtained and there would be
but one neutral plane, the same as in any homogeneous bean.
However, there was a very small slip between the concrete and
timber sections, as previously noted, showing that the true
condition lies somewhere between the above two extremes, so

it would be expected that there would be two neutral axes

T

‘ “ o ‘I _ _ 0
Bulletin No. 1, Oregon State highway Department, po. ol

-

-20-
quite close to each other and to the theoretical axis, de-
termined by assuming an entirely rivid shear connection.

As the conclusion drawn previously by the Oregon State
lighway Department indicates that the fype 3 and Type h.shear
connections between the junction of the concrete and timber
composite beam is more preferable than the other types of
connections. Therefore a study of the neutral axis of the
compos site bemns will accordingly restricted to these two types
of shea r connections.

A discussion on the shear slip effects the neutral axis
of the composite be we in the research by Oregon State Iighway
Department for the composite design reveals that if the shear
slippage were evenly distributed throughout the outer third
sectors there would be no slip at the load points; but, pro-
ceeding from the load point outwardly, the slip would be cumulative,
each increment being added to the preceding increment so that
the total end slip, as measured, would be the sun of the slip
increments fro om each load point to the end of the beam. Were
this condition to obtain, there would be no slippage between
load points, and the two neutral axes would coincide with each
other and with the theoretical position as obtained by applying
the ordinary transformed section forinulae . This means that if the
more positive types of shear connection could be secured the slip-
page was not sufficient to materially modify the general stress

distribution and that within the range of accuracy demanded

YT.

{E T80 “hi-cal E>u118tin 1‘10. 1’ Oregon. State flic'lhr’ly Deodr‘tlflent’

-21-
in designs of this character theoretical formulae may be safe-
ly employed.

From what has been said, it is permissible to use the
ordinary transformed section formulas for the neutral axis
in the composite design if the shear connections are of the
adequate and rigid connections such as the connection con-

sisting of combined Spikes and daps.

Temperature Effect

Before any discussion of the effect of alternated teq-
peratures upon composite design of this type, it appears
necessary to arrive, if possible, at some definite understand-
ing concerning the coefficient of thermal eXpansion for Douglas
fir timber parallel to the grain.

All in all, the data in reference to this prOperty of
timber are very meager and perhaps somewhat unreliable.
Koehler in his "Properties and Uses of Wood" makes the state-
ment that "different investigators are not in close agreement
in their results for the thermal eXpansion of wood". Studies
by Hendershot of Syracuse University indicate that the density
of wood has little influence on thermal eXpansion, but that
the presence of moisture may increase the thermal coefficient

to a considerable extent.

Hendershot's experiments did not include fir timber, and

[—30

their only applicability to the case n point is by analogy.
Furthermore, the data do not include temperatures below freez-

ing, and it is felt that the eXpansion of the moiture in fair-

-22-
1y damp timber as the temperatures drop below freezing may be
suff cient to counteract, in part, at least, the con,raction
due to normal thermal movement in the timber fibers proper.
Mr. J. Elton Lodevick, in charge of the section on Forest
Products, United States Department of Agriculture, makes the

following sicnificant comment:

c
\J

H (M,-

lc point, however, should be borne in mind in this con-

nection. Increase in temperature will cause exoansion direct-

J.

a

ly but, at the same time, the increased temperature tends to

decrease the moisture content of the wood and the decrease is

iwayr accompanied by a decrease in size. From the meager

31)

investigations available it would seem logical to disregard
thermal expansion in view of the larger shrinkage occuring
during drying".

ATGIH the Smithsonian Physical Tables for 1929 biv; a

f
U

va ue of 0.0000021 inch per inch per degree Fahrenheit for tie

coefficient of thermal expansion for wood, but no data are at

hanr 5 the physical condition or 1he moisture content

the Spec izn ens .

In View of all of the above facts, it apiears the part

_ I
A.

of wisdom to investi ate the phenomena deveIOpcd in these

composite designs in the light of two hv oiteses: (l) the

I
§ )
J.

Smithsonian coefficient (0.0000021 inch per inch per degree
Fahrenheit) and (2) neglecting the thermal eXpansion and con-
traction of the timber stem entirely.

9-.

In the tests of Oregon State fliShWHy Commission on com-

’

O: (-21" f: 13’ t 5". to )‘II'; I“ 7

.I-
Ll'(':'3
a

. 3 ,
111' 1")

‘ ‘ ‘~ " ' >-- - , ' r ‘ .‘ .- ~ - r r...‘ ' , v r‘ ‘ ‘ L 1 ’ | o » "
I~'fiI‘II‘;-"iL’;-1_.I_I.L'Ii’. F‘NJr I‘z-UI-E. itiuLIe‘i'a 1,111 e CIIHIILJB
‘- 1, 01 _ o .. _ . ‘ D ‘0
HM?» (318131 lI/l‘l;“() I IN l...U {Mtg/S ES 10110‘It:
—" . -. .. ,- -I. ,. o ,, ‘ ,I .- _. ,w
TAJI‘ TIQI' 1,21. YUM/e: :Ié-eII I. UL (.LH‘M-l *7. LC) c. In

tilimx“ at. {In funct'm‘m of these TAO IIItIi‘IHI'Jiilfi, F-M'lI’lit‘iI';I3'I:-:l
slut-wer'In; s1:I_rj':...II-~s are induced Inhjxih must o‘:‘I\.iou.~31y be pro-
vided for by increwsin; the strength of the shear connections.

Sr. c on d. by v i rtu

J

stresses are set

fibers
of tflué CMLCTWBLC

Th e r), r) n c 11}

w
h

"I t Icon]. (‘2 app e I; r

- ,. 1-. 3 . —.
imam? LIC} in? )b‘

-_ t

to

posits beams of
the Ulrietjmq uni

, ”I J
1)}; tale/I

- ,1 _‘ 1 , ,.
‘.' Nerf) .LIC 3' tilt) in
'1’1 _1 .
at : LNG III
1. _.
JO = trn—t i,
A V
n = {—‘II’HH

O

0.1

e.

. 1,—
5",1‘.

ion d°

+2“ .F. 1': t

tivate

U

- - , '1
Quail

1‘3

0 f t h e

7.1613 86100 mi a yv been ("I "I_ I I , it. I—a’JIiI'I' .9, 1" a huge
V g.) .L
lCh become a maylmdm at the extreme

II‘I tirrilwl", LII’ WOI’fi'lS,

and. at the bottom of the timbe-

awn. fPO‘HI the eliove

t“. Ie only 1: e .8 tt re

in 12““
J-

__1 _o_ \ _ '_ 1... _ .. o . 1_ 1_ j ‘ y , -D ,__, _.
II .|_.Il conmac lIJ an \'.'_L in) t: LI III‘ r: I a" (._)l Goa -
. -0 ,_ .. , _ , V - .9 , . _. .’ , _ -.. .-
7JG ‘JIHTIIWIEWI 7 n t‘Iur: II1\€AsiILI'Ii,Ler1 ai‘e
J. U

-, . , . .1 - , -. ., ‘ 'I .. 1 , :I ,\ r . _ n I ‘.
zinc. :». (I I L t. gfl‘ {_,1I"_(Zf\.(“. ‘3} 'UL) J :7 {Ir} (25:4,.«1'. I I. r I 6;)(3

ate:
23p Cc t
..~C .-
17'
“‘C "c
1 + ---——
A ‘71
"I'.‘1 ’
at
C
TI, = ----
S
of elasticfiy for the coI'IcrILIte flange
of clastieitg’1<w‘iiie tthcr Heb
com fr: c I ent for com‘:‘rI-.zte

0117(3) fr ‘3- 86-3013 I (In 0 I com (“I r I: t e fl :3..I“I£;e

rm]
,,

A : area Of the CPOss-Sectimn of tihber stew

1”)
O
I l

ber stress at the ‘I:Iot1,r.I“r-. of t- Ie concrete flt‘flLjG

at tne jIJ.I‘II‘.:t.;'I.<‘>I1 "point at the center of the );.",‘I'n

F131
O
I |
£12
'--I
J)
71‘
0
C1.
\‘I
r.
i...)
U:
(1'
H
.4
TD
U}
(D
[._J
,3
O
I.
,..J
3
P3
7)
:‘1'
ID
1-
1...!
3
“\
3

In the abI.ve formalise the ter-II "n" I’M'IIPQ nts the nurrlber
of shear conn.I=:ctiI:Ins whic I. 'I‘:I'I.Ist be iaI‘IIVlH d for tr: IIrIIiIm
stress (the51, of COUI‘MR, to be in an.Iitio on to the connections
nec:ss:.-Ir<r for the tr: st-zr encs oi load. stress). ""7 e ter..21 s
1"011I;z"I-_IseI‘Its the value of team shear cormeI IIIII, and. the term
"t” retresents the lij.«':i.}i'7...iillliil run -, in tcm")erIr-atnre from the as-
sw‘neI’l mean or construe tien t oci‘oItllrc.

I would III {e to quote the .(TOHI'11L'ISIIUTIS I'iraxI'III mg by this
study as follows:

"Variati-zx'ls i‘I'I t.s-;.I"r:e:mt'ue i‘l'(;)(‘11).C(—.3"1 stresses of an

J-

° _. .. .. -. .9 . .- ._ ., -. .. _ - - .0 I- , ._-.- -.-.- .9 n, --, ,_
Cilxsrlt. UJHiJVl'1ILU1f3 LI) \ueIPI‘erlil ti IIIfi' irIf‘ttI )I‘C)v1.b tuNl IIJI‘ 1,1m3 Sniule

. l ‘1 ~’ ("- ‘. . “I m1 ". n~ . ‘ Ia ‘ 1' ' " " ‘ "o l "v ‘ 4' .‘I 1‘ '\I" I ‘\ ' T l 12' ~ '
1:1 1:511.3_1.Qsl.]1_. i fidtkll a, Li(1-¥e\/H] ’ C41]. ‘1.)() C-.\1('f*‘i‘.1';1.—t/‘L'1 ‘1 tiff-Mikel].
~ . I" - .- - . ~ .1- .n _ . . ._ - . (— _° - -. .. . ,, ‘I T ( ° ‘ . .,~
0 are Oi 1J1li°£)upil :gI iJL'Oi) 6-: P :12: '31-er I f 1",} II: 531117? CI... ‘ connec tltfll. T11.)

- -. 'I _.. -., -0 .--n.4:3. . ,_‘ ,'__‘,,_ 3 ..:I, . ‘....‘_,
apfear to in‘ lune stress oI sqIIItleJt magnituug t; c U39

concern; hofievaw5 iflweIWBVQlaneut of tension due to 1Is1raInt

visabili 1 of an III‘leInvite liIe'I“rtr:':'IrI1f,I-=: e of ion i1‘.I,II‘Ii"‘.II.<Il. ten-

U .

\I
—-

perature rei rforc e III-mt" . "

‘5

Te c‘I'I

r
It). :1

‘i
LA.

I ”‘31 13.111191'1‘fl 71C). 1, Ozf‘I'L-‘wrfIII 31‘, H.361,1?;1'1II.“-,';ey TH:I;_I‘("1,II:I)I]1",,

-1.
A1

Evolution of Theory.

Fran what has been said before, it seems, at this point,
it is necessary to develops the formula whereby the composite
members of this kind can be designed without resorting to
physical eXperimcntation.

In the design of this type of member, it is obviously

first to assume, as in the case of all T-beam girders, the

Cf-

hickness of the deck slab and then the transverse spacing of
timber stems. For short Spans, the thickness of the concrete
flange will probably be determined by the permissible minimum

'1 1

deck thickness (not less than 6 inches for modern highway load-

ings), and the spacing of timber stem or stringers will be de-
temnined by the transverse carrying capacity of the deck slab
exactly as in the case of a homogeneous T-beam design. When
the length of Span increases, a point will be reached wherein
this method is no longer applicable, and it becomes necessary
to increase the thickness of the concrete deck so as to provide
sufficient T-beam flange.

A reviewing of a certain empirical restrictions is
necessary at this moment. For homogeneous concrete beams, the
standard specifications of the American Association of State
Highway Officials provide that the assumed effective T-bean
flange width shall not exceed the following:

(a) One-fourth of the span length of the bean.

(b) The distance center to center of beams.

-26-
(0) Six times the tidth of the beam.
(d) Eight times the least thictness of the slab
plus the width of the girder stem.
Now assuming the adequate bond and shear resistance have
been provided at the junction of stem and flange, the effective

flange width assumed in the desinn calculation must be arbitrariiv

U U

'I

selected in accordanc with the aoove empirical restrictions.

{D

However, the composite beams tested in connection with this re-
search project carried by Oregon State Highway Department re-
stricted the flame width to four times the width of the stem.
It further st tes that unless more experimental work is done in
this connection the restriction regarding the effective flange
width (that is four times the stem width) should be adhered to.

O 1_
L

After the approximate dimensions of the composite mem“
having obtained in the manner as mentioned, it remains necessary
to find the method for the determination of stress. It is very
evident that the stress analysis involves two distinct phases,

that is:

S

co

(1) The evaluation of the extreme fiber bending stre
(2) The determination of the shearing stresses in the
junction point and the design of proner connection

“—1

mach one of the two above will be considered in order.

1. The evaluation of the extrer‘ie fiber bendinc" stress.
U

If an adeguate shear connection has been assumed to

rive a rigid and truly elastic jwnction plrne, then the cosposite

(
U

J

_,"7

-_‘-

'\

beam may be designed by transforming the composite section into

an equivalent homogeneous

CO

ection in the ordinary manner-wnicn
obviously consists simply in multiplying -, , .:-- Q.
width by the ratio of the elastic moduli of concrete and timber,
Ec/Et’ and thereafter trgating the entirely beam as a purely
homogeneous timber beam of the transformed dimension.

It should, at this Irmment, to be borne in mind that the
above assimption holds only for a rigid and truly elastic Sheer

connection. However, as stated previously (see comparison of

3nd Slips) that a certain amount of fleet

.__J.

2 ~ ~ ‘ n. n
c shear slipgage and

the consequent formation of two distinct neutral axes, neither

.'

of whicn is coincident tith the computed or an in-

H)

;osition
tegrel composite structure. The first ohase of this prohlom,
therefore, is the deterhination of the degree 10 filich such

4- J _.

shear sliliagc Operates to modify theoretical results.

The fLEUTES in the next gage were taken from Technical
Bulletin No. l, Cre;on State Hi;hway Department, show distinct-
ly the relationship of each stress nurv» to the others. hacn
figure contelns six curves (three for tensile stress and three
cor c mprossive stress). The pair designated as "measured

-H - 0 ‘1 -0. .. -~_\ $.43. .. _.N , 1 - V. ,. ,
stresses was obtaineo lVUM hue «w WCJHLLUQS actually Measure

'1 -. ~' "Q fl \ A "1 V ‘~ . 1 v , - V . D —\ - . - ‘ '1 .- -. ‘ .. .- ‘
flUPLMb the tests and,+nNénrmhfli oi elastictty as determined ”if

n 0 1 n - .. .n .. 1 1 ._ rm, . , - . ,. .1_- .1 "4.1‘, .. I- 0 _. -__ -. _
1N:”l'flfllhdJ:Lj JJDP (38Cz DeELfl. LiUQ CLJPVLHS madfl;0:1 LuuéOLWscitfinl .%sz,n

tvaient timber section and using toe actual values for the

AI1 o p ‘ o o __V_“V. 1 .___‘_o’r‘ ‘q _' 1. _': ,'_
Wha~HA -l (\i el-e¢3t.uciitnv ban LCIl . ei'e e; iwfil'iilflfltt;ij.5 éaei‘.WJ{LLfH9 , i113“

-98-
curves and the ”theoretical stress curves

are waged upon the Home moduli of eiPSthlt‘, SO twat toe

Varietion of these two curves shows the discrepsnfiy intro-
11:: fit-“re fit the (.2011:er ’61ch with small errors
.- 1. - , 1. . _ 5..“ fl -- r. _. . 1 0.... _ _ 1
..r1e.nt ‘..8 meme oeen infil'o'iLiuet-lo PPdCi-LCm-ilv in seen

case, the two curVes follow each other very closely. e8-

0
..

.un 0 within the working limits of the me-

.. -n— a-

, _ ,o i, is - .”,,, A..sm -i- ,'u - .W L. ,
Tllvé (’fi-D‘f]:!._‘.!l-‘-3'-’l fist/t J Ch L‘V (17-3: (3623 I CYL’J. last} 8.5) (31:38 LCD. S “I'QDS

have been produced in exactlv 1e some manner as the theoreti-

cal sfinwess cuxunes exccfflg bhflifi 231 essunwxiznodmflJis of Efleasti-

1

non for concrete and

H-

city (3,000,030 pounfifi p8? oCUHPG

1,500,000 pounds oer square inch for tinher) instead of the

l
actual measured one have been lsed. In this may, the differ-

ence between the "desirn tress" end ”measured s,re“s" curves

{0

not only shows the discrevgncy erisin; from sheer slit
and instrumental errors but also the errors iitroduced from

the variation in elastic moduli of the meteris s from the

0%
(I)
I

sumerl Values usually I»??1f)10ye:3.

n

t ioints out lrmn the test that "In extreme cases the

F.

S

:15

i
variation between "design stress" and "Measured Stress" amounts

5 Per cent, but that for the average condition

L“ J

to as much as

the messur

‘W‘
A

/ ‘ .
; tensile stress was 6.0 per cent below the seeign

- .-- . . fl; - . .c H o .-
stress, and the measured COWPPBsvae stress Was p.o per cent

o siress. It should be rememhered that all

1

assumed and actual elastic moduli are not peculiar to the

.Sfl655-/%anaG/aer:gnama?A706

5,1,3.”- - Pmpaé/per .57kaa/29 //7cé

000

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3 /
fi j}' a ffl’o
v 3, /
‘ /
a 4-" 7
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Composite Beans

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Ainzmrflfinn7 ' Aiaaa7flkmfla
§ 5/) at (in ’6’" in ' ' ’
8 .r. I? 3 64%?” ’2” ”’ I
‘3 .5/‘(Vlk‘5 J Da 5 \Q Q; 5) ,' 4?: p s J
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§ § §
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g //.91.‘ . \g § /‘ 0' .
‘ */ Q \/ lt} ' I
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Load - ”foam/’0’: of 511/703
72' 5, 75/73/75 511/45:
6 5’. Com/ram?! 5/"!!!

4040/- fiaIJanafit or’ 511%

775‘. 26/23/71 fir-ct:
C - 5'. ton/rest»: .9615:

-20-
If

coMposite type of construction but are inherent in all struc-

0 0 1 1. - ° 7
tnres bUth of these materials Wwetner homegeneons or COQDOSlte.

rrom what have been "aid above, it may conclude that,
waile there is some discrepancy between the measured stresses

and those «etermined by theory, the variations are not suf-

ficient in magnitude to cause any apprec’able error for mater-
ials of this cherecter. Therefore the thecretical cesign

formulae using average values for elastic moduli may be safely

used.

There is one feet that the errors er sin* by a variation

in the elestic pronerties of the individual msterials are con-

siderablv greater than those introduced by shear slipplce

'0.)

0')

points to the advisability of determing ,he elastic modulus of

both timber and concrete, whenever possible.

2. The determination of junction p6int.shearing stresses.

(

The shearing forces alone the junction plane between

V

timber and concrete are the horizontal shears due to dead
load, live load, impact and the shearinr force set up from
temperature variations. These shear‘n forces must obviously

be resisted by the connections between the junction of the

two materials. The provision for these shearin‘ forces em-

ploys no new principle. It simply involves the designing of

-v 0

connections Which are adequate in shear and bearing.
Since the most suitable shear connection as recommended

1

previously was the combination of SpiKGS a

,3

d daps — type 3 -

I

-31-

For the present the discussion of connection will adhere to
this type of shear connection. However, in the practical

‘ ~3n the snear develoners will be used instead of spikes
and daps, because of its simplicity and economical,and, cive
just as adequate and rigid connection as spikes and daps.

For all practical purposes, it may be assumed that the
entire bearing stress taken by each Spike is concentrated in
that one inch of length on each s’di of the junction plane.
Such an assumption will be safe and will give reasonable re-
sults, and, for ordina y commercial sizes, it will be found
that the factor of bearing against timber or concrete will be
the limiting one.

In connection with the use of spikes (and it should be
remembered that tdis type of connection is recommended only
in combination with dapped joints), a maximum spacing of 6
inches should be employed rewardless of the theoretical

umber required to take care of the shear. A very important
point in connection with the use of Spikes and daps is the
necessity of driving the Spikes far enough below the junction
plane to reinforced the timber stem against failure by longi-
tudinal shear in the timber fibers proper.

In the mechanics it has been shown that the shear on any

cross-section of a rectangular bean is distributed as the or-

dinates to a parabola in accordance with the following fomnula:

S C2_y2
so : - --------
V I 2

-32-

where sy the shear at the point in question.
S : the total shear over the cross-section.
I : the moment of inertia of the cross-section
about its neutral axis.

0 a distance from the neutral axis to the

extreme fiber

the distance from the neutral axis to the
plane in question.
The shear is, of course, a maximum at the neutral axis,

diminishing in ac ordance with the above law to zero at the

O

extreme fibers. It is apparent that there will be a plane
somewhat below the neutral axis, at and below which the re-
sidual shear can be carried by the timber itself at safe work-

used in th

to
(D

ing stresses. The Spike

J.

junction plane connec-
tion should obviously be driven to this point. They should
also extend upward into the concrete about half the thick-
ness of the slab and preferably not less than 3 inches in

any ordinary de31gn.

-33-
The Practical Design.

Before taking up the actual design of the timber-con-

crete compos1te deck a brief summaries of what have been

said is necessary. The dead load and live load stresses

must be segregated and applied to the preper elements. In

continuous beam or slab construction the distribution of

bending moment between midspan and support will depend upon

the elastic preperties of the assembly. In order to deter-

mine the position of the neutral axis, moment of inertia,

and section modulus, it is necessary to transform the assemb-

ly into a hypothetical wood section, which is done by multi-

plying the steel area by the ratio of the modulus of elastici-

ty of steel to that of wood as eXplained previously (which

is usually taken as 18.75 for southern pine and Douglas fir).
It should be noted that the critical condition for which

the member should be (design-ad exists when the slab is first

placed in service, before the concrete has attained its ulti-

mate modulus of elasticity. Consequeztly, it is necessary

and be conservative to treat the assembly as a homogeneous
timber beam throughout the reaches where the concrete will be
in compression, that is ECZEt. As in continuous spans over

supports where the timber sect on will be in compression, the
ative bending moment is resisted by the steel in tension
and the timber in compressirn. The concrete is considered to

have no value in tension.

The entire dead load of timber and concrete falls to the

-1!
J!

I‘-

timber section alone, and not to the composite assembly (cen-

‘

tering for support of composite decks mvy he FEflUlTBO in ex—

ceptional cases).
The calculation of stresses for dead load in a continu-

ous Span construction will depend upon the relative magnitude

of the pOSlt‘ve and negative bending moments at critical

points. However, because of the joint

U}

in the tirr ber sub-
base, there is no known theoretical basis on which to calcu-
late these moments in accordance with the action of a con-
tinuous beam of variable moment of inertia without resorting

to

W"

(

{cttal loading tests in order to determine these factors.
Such tests have shown that for a continuous timber subdeck

with ioint as above described the positive and negative bend-

0

ing moments for uniform dead load in inl*,,:‘-:n..or spans are very
near y equal. For all practical purposes, each can be taken

as 50 per cent of the simule Span dead load mowent and they

0
1

occur simultaneously. Pos;

C1.
f—o

've moment in end Span will be
slithly greater, usually assumed at 60 per cent of the simple
span moment.

The live load stresses are resisted by the composite
section. In order to detemuine the forces acting on a given
width of slab it is necessary to fix the lateral distribution
of a concentrated lOad. Tests by the Maryland Sate fioads
Commission show a distribution of 15.1 ft. for a single live
load placed at the center of an ordinary trestle.* then the

effect of passing wheels placed in accordance with standard

clearance diacrams is taken into consioeration, the lateral

fix

iistril‘mtion for a cri 1111031 concentrsten load is 5.1 fBQt,

(bv critical concentrated losd is one of the interior heavy

1

wheels 0L two pessin load units in accordance with standaro

i?“
U
clearance diagrans).
It has been cust mary, however, to assume a somewhat
narrower load distribution for shear than for moment calcu-
letions, sirce the critical position of the load for maximum

shear will he closer to the supgort. Thus the distribution for

shear celcvlations is taken at h.0 feet and for moment at

J

F0“ live load, the positive moment is taken as 70 yer

cent and negative moment as 50 per cent of the simyle span
g

live load moment in interior spans; and o, per cent and ho

per cent, respectively, of the Simple Span moment in and scans

.L‘

and 2-Span structures. Laximum positive and negative moments

do not occur simultaneously.

forking stresses:

Timber: According to grades specified, viz., 1200f,

/

1300?, or loOOf.

"S
(D
H.
'3
(’3
9- J
H.

Concrete: SoO lbs. per squa n compression
(some designers use 300 lbs., which, of

course, give a somewhat higher resisting

moment for the midspan composite section.

.'I
0“

Proc., American ”ood—Erxserver's Association, 1939, pm. 272

r .L

-16-
steel: 19,000 lbs. per sguare inch.
Shear Us‘avelopers: 17:30 1‘08. €530,111 1°01“ 3, 32 in think
gteel lete in groove 2 inches or less in

W 3. d th 0

The following is the detaile calculations for a l-span
tinher-concrete composite decks highway bridge with 2h ft

roadway. The two end spans at 19 ft. from back face of

’W

abutment cap ti center line of first pier (17 ft. 6 in.

center to center of bents). The lfltOPdOletG span is also

at 19 ft. The total length of bridwe is Sh ft. back to back
of abutment caps. The bridge is designed for the standard
H-]_5 lo afling o

The tinber sub-base consist of alternating 2 x h in.

and 2 X 6 in. plank laid on edge, spiked together with a

concrete surface, increasing from 3; in. at the curb to he
in. at the roadway center. Crown is not to be less than 1

in. All plank are dressed to a standard thickness of

1

1

-5/ in. :ne top and Jottom surfaces of tne wood lanination

CO

H e4

ie in true horizontal filanes in order to ma ntain a uniform

I—I

depth of groove.

The shear develOpers are used for the shear connection
between the junction of concrete and timber base.

A one-foot width of slab is assumed in the calculations

as follows:

Timber: Average hickness ........ h-S/R in.

weight ................... 60 lbs. per cu. ft.
Concrete: Average ,hickness ........ S in.

Height .. 150 1‘3. per cu. ft.

Total dead load is:

)9 {"2 "Cl
Timber: e£i33 X o0 -1 $3.1 lbs. per sq. ft.
C.
[J /' 1
Concrete: -4-- X 150 I 02.5 108. oer sq. ft.

 

Total )5.0 lbs. per sq. ft.

Simple span dead load moment for 18 ft. span is'

-____-_____-_-;---;-- = “1,500 in.-lbs.

.

For interior svan this moment is distributed:
Positive moment : hl,o00 x 0.5 a 20,800 in.-lbs.
Negative moment : h1,600 X 0.5 = 20,800 in.-lbs.

Beam.elements for 12 in. of slab:

Hood section at mid-span:

here

*1

fire 0 in. of width for each height of laminations.
then let y is the distance from base of the lamination to
center of gravity of the section, we have,

6(5.~25)(2.91)+ 6(3.62S)(1.81)

 

 

. 7,
6(1.21)3 L4 ‘ ‘ if,“ ’3
m 1 m
12(2.3!2)3 ll/aa/Secflb/I 1664/22/50”
-------- : 56.8
’2

o 1'. o 1 o o
.5 in; 13 tue moment of inertia
of wood only

Tood section at Suggort:

Since only two-thirds of the plank strips are continuous

.—

port. The moment of inertia is therefore 2/3

. . h ‘ f ‘
d = g X 12630:) = S’HOJL lh.‘ b N I
C. 3 ‘ ‘ ‘

'm
M“ ——-- --

of the mid- Sfen section, or

21's
fiwfiu/
Akw

E“:

 

 

 

 

Where y : 2.};2 in. L 2
J__
Connyosi te section at mid-span: W5ec/xbn afjappor/
FTT'

inis section is considerefl homogeneous, therefore y is

 

I r——/2f———91 \‘
e o‘-"'.,' ' 14 1‘: 2313,23; § v.”
1 (1 )3 .3, 3;..- \gg
I3 : """""" " ‘V 3; 335.3: 4 ."3 1‘ ‘ ‘6 h
12 Q ~N .‘4. ‘ ____,_\°‘ 2
’l “in ‘2
. 0‘
. in“, in; l .3 i

 

 

 

Composite section at suoport:
Same as before, because of joints in the plank strips

at supyoris, only two-thirfls of t1e l .Inatlons are effective.

Each hci;

therefore

two.§/8

burs

tnen,

t 0

Let

ht of lamination in a 12 in. wid h of slab has

a width of h in. It is further sssnmed to use

in. round bars ov;r suppoct between longitudinal

take care of the negative moment.

-jg;émuwnrr:

           
 

yo htiifire flistefuwi from
Q

\1‘. ' 31.3: :3: 5‘“

rwnitrmfl 5n<is 'to ;€t€nel, ‘

.0
. .‘D a.
o

y be til?! (3 .1 Sta no (3 fropl

C‘f'

neutral axis to the bottom

of wood.

 

2.S(”.06)+ meme) + one; x o
v - —————————————————————————————————
as "
2235+ 11%.}? +209
I” g"
1050 area/x v.75 .- 20.” wool
: 30:)? 1110 1"; *+
N
_- h

 

 

 

 

 

)L— oooooooooo Co

—- ------- - 0.0.0.0 11000
'3
.2

’:(3.63)3

x’!.(3.‘*:.)<?.5§)2.. 111.0

 

-’!‘O ..

Tension et mid-sgen: ff: —-- -----------
J '1. r'"
lc-€1.:/
= 3}8 lbs. per sq. in.
O _ If)
AO,\I‘OO )x K. '(
Connveusion Ht sugoort; f = __________ _--
t nL )
”H‘W
r"’ I. . - - .-
: L)‘:'k) le. ‘ kl. Si. J-l-l.

Live L010 Stresses.

8

', _ _ _ F1 1 _ _ '7'." H V _ V Q ~ 1 n A "T F"
For the stunfiard a-ly loaflin; of tne d.k.3. .0. a lp-ton
truck with 0.H lOed on each rear wheel

1

U1
1
I

A 2,000 x 0.H - 12,000 lbs.

This load on e l—ft. Miflth 0f slab is

_ 2,V00 lbs. per foot wiiih of slab

: .
For Sllnle syai wmnent
l
--- x ?,000 X 19 x l? = 129,600 in.-lbs.
H
Positive moment (lhtCPlOP span)

Negative Imgmient (ii‘JtoTniOI‘ sugg=zt)1*ts)

129,600 X 0.5 : eh,800 in.—1b8.

10.. «
mld-SPHH:

on in wood:
, r-’ 5.
)0,7?\, X D.j\)
10 -- - .0
t = —-----—---—-- : M40 lbs. pen sq. in.
’ 1fi’)‘.

.l \lr'_-'
I

H.)

Compression in cancreta:
/
fr. : -----———"-""- X 1.3) a 5%.: 11):}. :{WVET} S ‘0 1r].

Tension in

*‘b

C!

"n - - O r"
hrlf'j‘e) It .79
m! .. -. .‘
l .L' :1th .

Gr.

.1 liq-Spa

Ifiri-snis
L
811001.
in b:rt

A
."N ’._CQ
fit.) )l'-.3

102‘";

'Hie 30 fwfi*<3ent iruwmzt ellcwenu 0.

wood:

L‘. O l “(a
0w,u00 X '.;0
‘ ' L A -c _ - a
————-———————— : \J-v‘)'\’ ]_‘}‘I:j. i.)\;1° 8(1. 111.
Mtg
ll l-’
. , .fi
stool:
'0 :x 2.52
o (‘er _‘ A H 1" t 'p
--————-—-————- X 3 .::‘ [K 3.3 = 1L, \\;\1 1').C\. ilf—Tic
.1.) e
'1 l-x
.. —. /”~'.~‘
— J .4
S .
'~ .9 --. n-.‘l-: 1 J (1.1...- .~ ‘. .
infaxrimm o Mimi .;n.l‘¢:‘rrr..«.\-,.‘>
- n0 I10 0}... #1-: 1--.- .
[1: 371+ .‘lk' I “.‘U inf-n. flux full. in.
[—9.1 ’fié. fi'fifi 11. 1-- ,., .0,
3 ’,}9\J+ O;I\J = 1,: ’5”,— _L.'L 5‘. L‘Hf‘ ‘4‘10 1.1.10
- rn-4_ 1 1.....- .9... (”O/'5 '11. - .
(1: J,i._)lu‘i_b_ Stress 1,.1’!\.n'. 4.05.». p91” 81. in.
I ,— 1 ‘~‘t“‘}"ll k"! N 1? flap 1“! ' f' ifi’N .-.
. tUI '-L o .10. is _,,’,~.,\,- In . m 1;. in.
(1, _r 0 -,_ .[I r11, _ _ “W -- ‘1 ._.l_ -1,
“Difi"i\\]_|!.\ OJ- |)1L(‘>I 7' U'I.’VQ _L(-)\/\ ; .\.
U A
V- 0.1 ,0 _- 4.1. -1. _ s - .-‘ ,0 7“,)
been 9:10 bHLOm: MM: :1 ‘HuP CO I‘leu'fi 1:1 Is tlv 0:9-‘ien

 

] :1'7n 1,0,» l 0'17 3. I» 171%]. (l l S 17‘!“ 1.101.141; lull 3, 9. i1; :3 T} ‘3 lot.
Orlthfl positiun of 10:3 unit fo co.wut70; s ear will
at {lnHW: times the (Hqfl31<if slab free suffmnizzia specified
Service Bureau of American Wood Treservers' Assocwetion.
tiis cese it is about 2 ft. 6 in. Therefore;
12,000
Effective 1060 per ft. wiflth: --——-— = 3,000 lbs,
.1;
lldllirlfi'i' 30 120a? cell-til i 098013 c o o o o o o o o o o 900 1173 0
Total 3,900 lbs.
1, C
J.’)."
End Reaction is 3900 X ---- ; 3,3:0 lbs.
I
“r - . , I" l. r’ . L r"
uflt Section. (12 x 10.12) - 2(p.o2p) - (2 A 3.02))
- 3-02. F; 8'11. ill.
(flote' Splices eliminate tco lewinstions from
t‘zie section)
3, 360
Average unit sheer: --—-— a 33 lbs. oer Si. in.
1.02.5
Hexinut :1 Sheep st TJeutre 1 AK 1, s:
. H , H i W _ fl -
33 .( l.;) = lt}.; llih. fwn“ 3H0 :Ln.
Totel Horizontal Sheer on l sq.-ft. is, therefore,
, ’ Fl r "‘ ‘»(‘
l9 9 r) 2‘. 3-’:-/ 3.. - 7]. 30 111.3 .

(‘1
k3

Sheer Developer

7130

2:0

17,)

PQTU1P9d per sq. ft. of contact eves:

h.l

oincc there are ----- A - : 3.69 grooves per foot of

o o 1 r-’ 0 ¢_ . -1! -. . .-
w1dth (Witn 1—3/9 in. in s,vlps). The number of

'4.

’uirec pep linear foot in each groove is:

lue Spacing in each groovw is, thePefOPC:
1’?
I...
1.11
FTTI

loe SpaCin; is neifitainefl near the support where the

wear is a maximum, and increased to 10 to 90 in. at mid-

\J ‘L

6.

liorfl116n“
1-?2/30

L111] 4(_

L‘) so—I
2ft“

Belflock

fiunsan,

lguz.

T imb e 1“ -

1
1951.

“.Food Pre
1013.

It]

1’ I W131 "x"

v-r __
'11,.1
“ ’ U

se1*vi*iv‘ "(n13
U
1. HT‘ (frl
- .0 - "_0
StPU_C Wtd?en. 01 Deutfl3gl Rip
'JeSt C025 Lumberfiew's ASS

DThTT‘rVT A‘fiTfir
A).L L' \ ‘XAF'iL
r,
F.
The P?opevties and Uses 01 000
L. “F. 23N("TPripeP, fl. 1?.
- 1 1- 1 fl .- .
food w010uCOK, 11.3. Deterfiwue‘t o: Eogfiiculture
- ’ N ,1-
0.3. and «ouwlloubu, C. F.
10”diflL TCStS 0” ” 7“W “0 posite—,Spe Short-
SIDRTW I1igfl1vnfiy"Fmei(1Lfe .nynflwiwiirw; Ccnicxéeize 311d
0 0- 'fi ,. . . - -- . '1 . 7 “
Timb:r 1o plaxure, TUCHHlCH.l uLlef~n o. 1,
._,. . .1 _. ‘I
(W‘RLA)O 53t212, EfiiilvH-1J ijfitz Pf‘ LHrH,

Concrete

ASSOC

“Fodtuni Tinflmer
Association

A {.1
[.__/Ouli‘o U -

fiervice Pureau, énerican

ietion

‘Yood—Ppes

Bogincerin;

qorJEBIQS'

KUUM uh: ONLY,