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This is to certifg that the

thesis entitled

A Roof Framing System for Story and one—half
Residences

presented by -

James W. Goff

.‘

has been accepted towards fulfillment
of the requirements for

Mast er of Sci. dflmfiein ngd Technolqu

p.241;

Major professor

Datefi—‘fi 21; l4fl”

0-169

 

01115111

1464

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MSU

LIBRARIES
.—_.

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES wi11
be charged if book is
returned after the date
stamped below.

 

A ROOF FRAMING SYSTEM FOR STORY AND

ONE-HALF RESIDENCES

By
James Tinthrop Goff _

r‘

4;,

A THES IS

Submitted to the School of Graduate Studies of Michigan
State College of igriculture and Applied Science
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Forest Products

1952

TIBLE OF “Orfifio

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.Lu)..S k; 11-4 lILLIK/Q-JD I'qu-.-I..G U—LNJJL-JJ..&

III. DESI—H CF EWII'WCC: CIL3.R

do

IV.

Design of the Trial Section
Accurate Design Check of the Trial Section
Design of Joints

Design of Stiffeners

C"T nifélYSIS .x- D bLLJJM SLLE

V. CL""UQ

7-4 -fi \wfi"
Lb JL J‘L—JL

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03 'Q L“ H

3.:

16
19

23

. *f‘Tfl'thp'pnj" ‘5PT~,’TS
{surly .: #UA.“ u‘x

The author wishes to express his sincere
thanks to Dr. A. J. Panshin, Head of the Department
of Forest Products, under whose guidance this
project was carried out for his interest and con-
tinuing encouragement. Thanks are also due to Dr.
Pfilliam B. Lloyd, Assistant Professor of Forest
Products, and Ir. John L. Hill, Instructor in the
Department of Forest Products for their helpful

suggestions and assistance at various times.

INTRODUCTION

The idea for this design was born because of the curiosity of the
writer as to the cause of plaster cracks in the ceilings of story and one—
half houses. These cracks seemed to occur almost always directly under
the knee-wall, which serves as a short vertical partition in the upper
rooms of such houses, as shown in Figure 1. Little investigation was
required to ascertain that these defects were caused by excessive de—
flection in the ceiling joists or second floor joists which, through the
knee-wall, were carrying a portion of the roof load not meant to be sup-
ported by these joists. Under normal conditions of loading the excess
deflection because of the roof load was negligible, but after severe
snowstorms or during high winds, the roof load increased to an extent
sufficient to cause enough deflection to crack the ceiling plaster on the
first floor.

The direct solution to this problem lies in merely increasing the
size of the second floor joists sufficiently to carry this additional
load without excess deflection. In the analysis of this problem several
difficulties are encountered, however. The roof rafter in this type of
house is an indeterminate beam resting on four unequally Spaced supports.
It is a difficult matter to determine the deflection of the rafter alone,
not to mention the difficulty of determining the deflection of the rafter
and joist in combination as th y exist in the story and one—half build-
ing. Such a solution is possible, but impractical, since each case
would involve different values and, as a consequence, entirely new

computations.

 

*— Knee Wa//

 

 

 

\
WW

 

P/as fer Chic/(5 Here U

f

Bearing
Par ff 7‘ ion

figure: 1.. Convenf/bna/ 12!- 5/-ory flame

The second approach to this problem was to investigate the design
of an indeterminate truss, with the members thereof loaded both axially
and in bending. Such a truss would be very similar in appearance to the
frame in common use except that each rafter joist and knee-wall member
would be parts of a rigid continuous frame which could be prefabricated
and erected in place as a unit. Such a design presents the desirable
possibility of eliminating bearing partitions in the center of the
building such as is currently being done in single story houses with
trussed rafters. Then this prOposition was more closely analyzed several
difficulties arose, however. Prominent among these was the difficulty of
mak’ng suitable joints between the rafter and the knee—wall member, and
between the joist and the knee—wall member. The required end distances
for timber connector joints prohibited the use of these devices, and
other methods did not provide sufficient strength. Another problem was
the necessity for either obtaining extra long ceiling joists or Splic—
ing the joists between the outer supports. The creation of a moment
resisting splice between two joists is difficult but would be necessary
in this case because the members are loaded transversly as well as ax-
ially. In addition, the indeterminate truss would be highly inflexible
in use. If it were desired to install dormers on such a roof frame,
great difficulty would be encountered where truss members would have
to be severed. It would even be a problem to install a flight of
stairs leading to the second floor since this would involve cutting
the lower chords of several trusses. The indeterminate truss was
drOpped as a possible design because of the above difficulties in

analysis and in use.

The third solution, which is deveIOped fully in the body of this
thesis, lies in the imposition of the entire second floor load, a
major portion of the first floor ceiling load, and a major portion of
the roof load upon two plywood girders or beams running the full length
of the building in the position usually occupied by the knee—wall. In
the adoption of such a design it is entirely possible as was mentioned
above to do away with the conventional bearing partition in the house,
since the entire floor load is carried by the girders to the end walls
of the building. The elimination of this central partition allows ec-
onomies in construction methods as well as gives the designer greater
freedom in use of the available space. A schematic cutaway view of

this preposed roof framing system is shown in Figure 2.

 

 

 

 

Ridge Po /e

 
 
 
 
 
 
  
 
  

 

 

 

Co New Beams (Cei/inq L/OI'57‘5)
5/70r7‘ Sfud Wd/i

 

————- P/y wood Giro/er-

2nd Floor .101ka

 

Raffcrs (These can be
Jp/iceo’ d2" fhis pomf
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Ceiling Jois 7‘5

 
 
   
   
   
 

\
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Load or; Wd// = 272 pounds per,/l'fl€d/ 7000f.

.v-

Fl‘gure 2 . Ob/x'que Cui—d’h/dy V/ek/ 0/ 0’78 dflO’OHGfi/d/f 57‘00/ Hem/I79 Sysz‘em

d. w. Goff 4-23-52

 

 

 

ANALYSIS OF THE across

SYSmEH CF FRnIING

For purposes of illustration of the method roof and floor loads
which are in common acceptance by building authorities were selected
for use in the-following analysis and the subsequent design of the
members. A roof load of 38 pounds per square foot of surface acting
normal to the roof surface was chosen. This total roof loading is
composed of eight pound dead load combined with a 30 pound live load
which is assumed to be either wind or snow or a combination of the two.
The second floor load is assumed to be 50 pounds per square foot, a
combination of dead and live loads. That portion of the first floor
ceiling which is carried by the lighter ceiling joists outside of the
girders is assumed to impose a total dead load of 14 pounds per square
foot on its supports. It will also be assumed for purposes of analysis
and design that the maximum allowable deflection is l/360th of the short-
est span. Since the dimensions of the roof which will be used in the
prOposed design are 2h feet by 30 feet, the maximum allowable deflection
will be 0.80 inches.

Figure 3 is a schematic diagram of the distribution of the roof and
floor loads to the girders. It is assumed for purposes of design that
the entire vertical component of the load imposed on the upper portion
of the roof is carried by the girders. This assumption results in
maximum possible load on the girders and is entirely satisfactory for

the purposes of design. From the information given in Figure 3, the

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beam diagram, the shear diagram, and the moment diagram for the girder
can be plotted. These diagrams are shown in Figure A. The weight of
the girders has been assumed to be 38 pounds per lineal foot, and this
has been considered in plotting the diagrams.

The rafters, as indicated in Figure 2, are of two by four inch
material, and are spaced two feet apart as are all other framing members
of the proposed system. To utilize standard lengths of lumber, the
rafters should be spliced where they bear on the knee-wall, as noted in
Figure 2. If this is not done, eighteen foot rafters will be reguired.
The ceiling joists which lie outside of the girders are also of two by
four inch stock. It can be readily assumed that neither of these members
is critical, but if the reader is curious standard references can be
consulted. (4,5) The second floor joists on the other hand are the
critical members, not only because they carry the greatest load, but also
because they have the greatest Span. In addition the deflection of those
two joists which straddle the center line of the beam will determine the
maximum permissable deflection in the girders themselves. This deflect-
ion is found to be 0.255 inches at the center of a two by ten inch joist
loaded uniformly at 100 pounds per lineal foot. If this deflection is
subtracted from the total allowable deflection of 0.80 inches, the allow-
able deflection for the plywood girder at midspan is 0.5h5 inches. In
order that the total deflection will not exceed the allowable it will be
necessary to limit the deflection in the girder to 1/600th of the Span.

As indicated from the diagram of the prOposed system, Figure 2, the
bearing load at each end of the girder is 9,150 pounds. The actual

length of the bearing provided by the two by four plate common in

W: 572 +38 a 610’°’/foot

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“3 3
9, Beam Diagram 53
51‘ or

' l
N + 9/50 “’5-

H
I
I
l , , 7 l
l
“U
.. 9/50 [65.
. Shedr D/dgram

 

 

 

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+ 823,500 pound-Inches ’
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residential construction is 3.625 inches, conseguently the beam will
have to be of sufficient width to create enough bearing area to support
the load. In a similar manner the stud wall must be reinforced at the
point beneath the bearing points with a timber of sufficiently large
cross sectional area to carry the transmitted load. It must also be
provided with a large enough bearing area on the underside of the plate.
It will be found (A,5,6) that a four by six inch timber framed into the
wall at each of these points will possess sufficient column strength to

support the beam loads.

DES GK OF PLYWUOD GIADEE

With the Span and the load carried by each of the girders known,
the design of the beam can now be undertaken. Several different
procedures are involved so the task will be broken down into several
steps. The steps will be summarized here and then taken up in their
prOper order.

The first step is the selection of a trial section for the beam.
The shear and moment diagrams are plotted so that the needed in-
formation will be at hand. The grade of lumber to be used in the
flanges should be chosen at this time, and it is convenient to list
all the stress values of that lumber grade for use in the following
steps of the calculation. With the maximum bending moment, the max-
imum shear force, the allowable extreme fiber stress, and the limit
of deflection known, a section which satisfies these conditions can be
computed.

The second step involves a checking of the trial section against
the allowable stresses, and the calculation of the actual deflection
from bending and shear. To accomplish this it is necessary to compute
the exact form factor and the section constant for shear deflection.

The third and last step is the design of joints and Splice plates,
and the design of stiffeners. It may also be necessary in this step
to design the braces for the tOp flange to provide lateral stability

for the beam.

Design of a Trial Section

The shear and moment diagrams for the beam are plotted in Figure A,
and the allowable deflection is, as calculated previously, l/o00th of
the span. The lumber to be used in the flanges is Coastal Douglas Fir,
Select Structural Grade No. l, as graded by the Test Coast Bureau of

Lumber Grades and InSpection. This grade has the following allowable

unit stresses. (5)

Extreme fiber in bending (f) lh50 psi
Horizontal shear (E) 120 psi
Compression perpendicular to grain (c) 390 psi
1,7 -\ r, ' 4 fl 6 o
modulus of LlaSthlty (a) 1.6 x.lO pSi

he plywood to be used for the webs is unsanded Douglas Fir ex-
terior grade, sound two sides, and the allowable unit stresses of in—
terest here are: (1,2)
Shear, in plane perpendicular to plies and
parallel or perpendicular to face grain 210 psi
Shear, rolling, in plane of plies, parallel or
perpendicular to face grain 5h psi
Eith these values established the camputation of the trial sect-
ion can begin. For any beam the flexure formula LF‘EEE' is applicable,
where E is the bending moment as found when plotting the moment diagram,
3 is the form factor depen ing on the section of the beam, f is the
allowable extreme fiber stress in bending, and E is the distance of
the extreme fiber from the neutral axis. The form factor is usually
neglected in solid beams because it is automatically canyensated for

in deriving the allowable stresses. (3} The form factor for the trial

(U

section will be assumed to be 0.80. (l) The deflection formula,

5‘13
381. T. 1’

ing the trial section to make allowance for shear deflection by increas—

is also applicable. It is necessary, however, in design—

 

ing the value of the deflection thus found by 25 percent. Since the

/\

deflection is limited to l/ouOth of the span it is possible to write

L = 1.25 x 5 U L

 

the above deflection efiuation as follows: -777 A, fl , -
" 000 pen a 1
'1'
Further, since 7 in this case is equal to ¥%-, it is pOSSlble to write
'- o

16Ff1
h

of the beam. If the deflection formula above is also solved for Eh ,

I 38' BIL
the formula JL= A ,,l
l.a5 x 5 x ode x L

 

the flexure formula as g1: , where h equals 20 or the height

 

2 is obtained. These two equations
can then be set equal and solved for LZh_and will give a ratio of beam
span to height that will satisfy both flexure requirements and deflect-
ion requirements. For the beam in question, the Léh_value calculation

follows:

L ___ 36141.6 2: 10° 3 a a
h 60,000 (0.8) (11507 °

For the Span of 30 feet then:

= 30.x 12
8.8

Standard four-foot wide plywood sheets will be used in the beam and will

h - Al inch minimum

provide a beam depth of 48 inches.

To determine the thickness of the webs the formula (1,5)
t.= lifig—E-, where 1 is the shear on the section in pounds, h_is
the depth of the beam section in inches, and 1 is the allowable plywood
shear stress perpendicular to the plane of the plies in pounds per
square inch.

npplying this to the problem:

- 1.2LX 943-50 _ lo: ' h

10

It is apparent that two webs of 5/8th inch plywood can be used to
make a total web thickness of 1.25 inches. This plywood is found to
have a total of 5 plys, each ply l/Bth inch thick. Three of these plies
are parallel to the long dimension of the piece for a total area of
parallel plies of 0.375 Square inches per inch of height.

'Tith the webs selected it is now possible to compute the trial
flange dimensions. The required moment of inertia T can be computed

from the flexure formula and is found to be:

.____1_:g_ = 823,500x21 2 1 100 . h 3,;
I Ff 0.8 x1450 7’ m" 8

It is also necessary to compute a moment of inertia from the

deflection formula:

l.25(600}51L4==1.25 x 5 x 600 x l§,2§0 x 3002
.384 E 38b, (1.6 x 100,

It is evident that the l as determined from the maximum bending

I = .=1A,500 inchesh.

 

 

moment governs the design of the beam. If the T provided by the
plywood webs is now calculated, the remaining 2, which must be provided
by the flanges, can be determined.

Iwebs = 2.x 0-375 X A33 = 6,950 inchesl+

12

Iflz Ib -' Iwebs

11.1 = 17,100 — 6,950 = 10,150 inchesl‘

By rearrangment, the formula for the moment of inertia will yield the

following:
hi = h3 _. ;2_l_ : where hl is the clear distance between flanges
w ..

I‘-

and 3,18 width of each flange, while ;_is the moment of inertia which

must be provided by the flanges.

At this point it becomes necessary to assume a width {w} for the
flanges. Since it will not be possible to obtain scarf jointed flange
members in field Operation, sufficient laminations should be provided

to make staggered butt joints possible. A trial flange width of

5

h Z-inches, which will be laminated from three l-g inch pieces is
U

8
selected. If the above equation for h is solved using the values
available the following result is obtained.

h3 = 1,83 _ 12 x 10,150
1 mm5

 

hie-Ah.l inches between flanges.

Solving for flange depth (d), we find:

=A8-MJ
d 2

Since the nearest standard lumber size which meets or exceeds

= 1J95 inches

these requirements is the 2 x A, the flanges will be laminated from
three 2 inch x 4 inch nominal pieces. Sixteen foot lengths will be used
for the laminations and the joints will be staggered along the beam.by

at least two feet. The trial section has now been completely designed.

A scale drawing of this section is shown in Figure 5. The various ratios
and constants indicated thereon are used to find the exact form factor
.and section constant for shear deflection and will be eXplained when

those functions are used.
Accurate Design Check of the Trial Section

Since the section has been changed in the flanges from that for
which the modulus of inertia was first calculated, it is now necessary
to calculate the exact g'of the beam that has been ad0pted. The i

as computed for the webs has not changed, but the g for the flanges has

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F l / ,H x 1
ll" {/13
_T_.
c ‘0.
22 w
N
N
§
*9.
Q
s.
I- - - ‘0.
00
V.
a;
g” ‘45 "' "g'
_l_ 4 ‘1—
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U

 

 

 

FIGURE 5. SECTION OF G/RDER

because deeper flanges than were needed are being used to correSpond
with stock sizes of lumber. The dimensions for this calculation are
indicated in Figure 5.

I a I webs + I flanges
6 950 ,_ 1.. 8750.83 -z.0. 753)

6 ,950 +-l7, 500 = 24, #50 inches
Computing the form factor (6,?)

d/h a 3.625/wa a 0.0755

tl/t2 = 1.25/6.125 a 0.204

F = 0.67 x 10/9 = 0.71.

The allowable bending moment on the beam is then:

13:.13EE. 2 0‘7A (1220) (24’A5Ql-= 1.09.x 106 pound inches.
c

This is well above the applied moment.

It next becomes necessary to check the beam for resistance to
horizontal shear. To do this the value of £52 which is the statical
moment of all fibers lying outside the neutral plane must be calculated.

Q = 2<o.375) <22.) (12) + 3.6251(4375) (22.19)

3 216-+ 390 = 606 inches3
The maximum allowable shear in the beam can then be calculated

from the standard shear formula:

210 4, .2 6 A ~
EYE—t a (21+ gggLi-l 5) =3, 10,6UO pOUIlQS

This allowable shear value is well above that imposed on the beam.

V:

Since plywood is relatively weak in shear between the plies
(rolling shear) the shear developed between the webs and the flanges
is of great importance. Because the shear acts on a concentrated

area of the web the allowable value will be cut to half of that indicated

13

in the table of values given previously. This gives an allowable
rolling shear stress of 27 pounds per square inch in this case. The
maximum allowable vertical shear in the beam on the basis of the

allowable rolling shear stress is given by the formula:

.319. EL.27(a,A50)43.6251 21.2 » .
Qfl x t1 390 x O. 25 12,300 pounds.

This allowable vertical shear value is also well above that which is
applied to the beam under maximum load.

The deflection of the beam must be checked to ascertain if it is
within the design limits. Deflection due to the bending moment is
computed using the equation:

db: 5 1:13 , 5 x 181300 x 3603 = 0.21.5 inches
31» E I 331. x 1.1 x 1.6 x 106 x 24,450

The factor 1.1 which appears in the denominator of the equation above

is necessary to convert the E'as obtained from static tests of small
Specimens to the true modulus of elasticity. It is customary to neglect
this conversion because of the fact that in ordinary beam calculations
shear deflection is not considered by itself since the value of §_as
used is computed from total deflection of the static specimen and this
deflection will include shear deflection. In the case at hand shear
deflection will be computed separately and it is therefore necessary to
exclude it from the equation for bending deflection.

Shear deflection is computed from the formula:

2
ds =- Pig}; C , where E. is the total in pounds,

 

“4

is the span in inches.
‘E is the section constant for shear deflection. (D

b'is the depth of the beam, in inches.

14

‘g is the shearing modulus of the
webs (Douglas Fir Plywood). g equals
117,000 psi when the face grain is
parallel or perpendicular to the span.
‘Q is a constant depending on the manner
in which the beam is loaded.
The values of'g and g for various conditions have been ccmputed and
plotted and the charts are available in the references. (1) §.is
related directly to the quantities d/h and tl/t2, and for the values
of these functions found previously Ki: 0.64. 'g is the load co-
efficient and for simply supported uniformly loaded beams Q is egual
to 0.05. If this formula is used with the apprOpriate values as

previously given the following shear deflection is obtained.

d_,. PlKhZC . 18.300(360)£0-6Al_(482) (9-05) a 0,159 inches

8 GI 117,000 (24,450

Total deflection is then equal to the sum of the two deflections or
0.245 + 0.169 = 0.414 inches. This is well within the allowable de-

flection of 0.455 inches.
Design of Joints

Joints in the web will necessarily be butt joints because of the
difficulty of obtaining scarfed panels of the required length and
because of the impracticability of scarring plywood panels in the
.field. The stresses will be carried through these butt joints by
means of splice plates running the full depth of the girder on both

sides of each web. The general considerations governing such splice

15

plates are as follows: (1) the face grain of the splice plates should
be parallel with the span, the total thickness of the plies parallel to
the face plies in both splice plates should equal or exceed the total
thickness of the plies parallel to face plies of the web, and the sum of
the thicknesses of two splice plates should at least equal the total
thickness of the web.

It was found earlier that the webs would consist of five-eighths
inch plywood which has three one—eighth inch plies parallel to the face
ply. From this information we may deduce that the splice plates must be
no thinner than five—sixteenths of an inch and that each must have at
least three-sixteenths of an inch in plies parallel to the face grain.
From the tables available on the veneer areas of plywood constructions
it is rather easy to select the prOper material for this purpose. (1,7)
While certain panels of five-sixteenths of an inch in thickness may be
adequate, it seems apprOpriate to use a heavier construction, and three—
eighths inch unsanded three-ply splice plates will be used. Since the
stress is transmitted from the web to the Splice plate through a glue
joint, it is necessary to design this joint with an area adequate to
transmit the developed stresses. It is assumed that the maximum stress
in both bending and shear will act on the same place in the beam and
the splice plate length is computed accordingly. The length is given

directly by the formula: (1)

 

'72 2
IJIV/(Fftla S- KVt) 3 where l'is the splice plate length in
r
inches; E’is the form factor of the beam
as previously computed; .2 is the allowable

extreme fiber stress in bending in the

lo

flange lumber; t_is the total thickness
of the plies in the web which are parallel
to the span, in inches; 1_is the allow-
able horizontal shear stress in the web
in pounds per square inch; t_is the total
thickness of the web, in inches; and S
is the allowable stress in rolling shear
(not reduced for stress).

If this formula is applied to beam in the problem at hand, the following

results:

l;[(o.7z. x 11.50 x 0.375)2 @x 0.625)2
54 ‘

l.= 7.85 inches
Eight inch splice plates of unsanded, sound two sides, three-ply,.three-
eighths inch thick plywood will be used. These Splice plates will run
the full depth of the web on the outside of the box beam and will run

between the flanges on the inside.
Design of stiffeners

Stiffeners are necessary in plywood beams for several reasons.
These are: to distribute the loads into the beam at the point of
application, to separate the flanges when the beam is loaded, to stabilize
‘the webs against buckling near the compression flange, and to facilitate
accurate fabrication. For the purpose of destributing loads, bearing
stiffeners are used. In the beam under consideration, the only bearing

stiffeners needed are those at the reactions at each end. The width of

17

the stiffener is controlled by the beam width and the only variable
involved then is the thickness of the stiffener (the dimension in the

direction of the span). This thickness will be found to egual: (l)

P
wc‘L ‘

 

where g'is the stiffener thickness in inches;
EDis the reaction in pounds; w'is the total
beam width in inches; and 2,; is the allowable
bearing strength of the flange lumber in pounds.
Applied to the case under consideration this formula becomes:

a 9150
. X €125 x (39041.10)

 

x = 3.A7 inches
The factor 1.10 in the above eguation is to correct the allowable bear—
ing stress for continuously dry conditions of use. These stiffeners
will be cut from naminal four by six inch material, surfaced on the
narrow face to a thickness of four and seven—eighths inches to fit
snugly between the webs at each end of he beam. It is also necessary
to design intermediate stiffeners, the primary purpose of which is to
separate the flanges under load and to prevent buckling of the webs.
These stiffeners should be Spaced according to certain fundamental con-
siderations, the most important of which are: the plywood thickness,
and the clear distance between the flanges. Other important considerat-
ions, however, are not fundamental to the design for strength and pre—
vention of buckling, but rather are closely related to the use to which
the beam is put. In this particular case it seems expedient to place
intermediate stiffeners at two foot intervals to correSpond with the

spacing of the rafters and joists which the girder will SUpport. These

 

1.
"‘"l
w

18

stiffeners will also lend lateral support to the plywood webs for the
purpose of providing a rigid knee-wall surface in the upper floor rooms,
and will make convenient nailing points for wall finish material. Dietz
(1) presents a chart giving basic intermediate stiffener Spacing for
plywood beams. Other works on the subject either make no mention (3) or
by-pass the issue with the statement that the Shear strength of the web
depends in part on the stiffener spacing. (2) It appears, however, that

the spacing as recommended above, at two fcot intervals, will be well

A

,within the requirements of the beam. Stiffeners of this class should

completely fill the Open Space between the webs, and should be contin—

uous between the flanges. A minimum recommended thickness for such
members is three-duarters of an inch, (1) and the ones to be used in this
beam will be one and five—eighths inches thick in order that this refiuire—
ment will be adeguately met. Two by six inch material will be used with
each member surfaced on the narrow faces to four and seven—eighths inches
to fit snugly between the webs.

Since the girder is held in line at the upper edge by the action of
the rafters, and at the lower edge by the floor and ceiling joists, the
lateral stability of the member is assured and need not be checked. The

girder is now completely designed and is Shown in Figures 6 and 7.

 

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l9

COST CCLYARISLR hKD ANALYSIS

One important basis for ccmparison between the prOposed system and
the conventional system of roof framing lies in the relative cost of the
systems. In view of the fact that the proposed system has yet to be
tried on a production basis it is difficult to claim that it will result
in labor cost savings. It is egually difficult to assess the increase
in value of the resultant structure accruing from the added flexibility
of design possible with the prOposed system. Two factors which enter
the cost picture can be definitely established, however. These are the
cost of the material needed in each of the systems, and the value of the
Space saved when the proposed system is used. The first of these is

tabulated below.

 

I Katerial Cdst Analysis --- Conventional Roof Frame

Hember fiumber and Size Feet, Board Leasure
Joists 32 pcs 2”xlO"— lh' 7A7

Rafters 32 pcs 2"x.6"- 18' 576

Collar Beams 16 pcs 2"x A"— 8' 86
Knee-wall Studs 32 pcs 2"x A"- 8' 171
Knee—wall Plate 12 pcs 2"x.h"- 10' 80

Totals 12h pcs 1,660 FEM

If the cost of No. 1 Douglas Fir (Coast Type) is @145 per thousand
feet, board measure, the material cost of the above conventional roof

frame is l,660.x 1A5 or $240.70.

II Iaterial Cost Analysis --- PrOposed Roof Frame

 

Member Number and Size Feet, Board Leasure
Joists 16 pcs 2"x10"- 12' 320
Joists 32 pcs 2"x A"- 6' 128
Rafters 6h pcs 2"x h"- 10' A27
Knee-wall Studs 32 pcs 2”x A"- 3' 6A
Knee—wall Plates 12 pcs 2Wx h"— 10' 80
Collar Beams 16 pcs 2"x h"- 8' 86
Girder Flanges 24 pcs 2"x h"- 16' 256
Girder stiffeners A pcs h"x 6"- A' 32
Girder stiffeners 28 pcs 2"x.6"- A' 112
Total Lumber 24h pcs 1,505 FBL
hebs 8 pcs 5/8”x h‘x 8"

8025, Ext. Plywood, Doug. Fir 256 Square Feet

7 pcs 5/8"x h'x.7'
3028, Ext. Plywood, Doug. Fir _§2&_Square Feet

Total 5/8" Plywood £80 Sguare Feet

Splices 1 pC' 3/8”x 4' x 8'
SO28, Ext. Plywood, Doug. Fir 32 Square Feet

Lumber Cost: 1,505 x 1A5 $218.23
5/8" Plywood: 1.80 x 0. 38 172.40
3/8" Flywood: 32 x 0.26 8. 32
$AO9.95
It is evident that the proposed system is more expensive from a

material standpoint. The difference is $169.25.

At this point it becomes expedient to consider the second factor

of this cost study, the value of the Space gained through the elimination

21

of the central bearing partition. An appreciation of this saving can

be gained by reference to Figure 8. AS indicated thereon the maximum
gain which can be realized is 12.h square feet of floor space. If the
completed cost of the conventional house is divided by the Sguare feet
of usable floor space a figure can be obtained which will approximate
the value of a square foot of floor Space. Assuming that the total cost
of the house in question was $12,825, and that the available floor Space,
up and down, is 1,026 square feet, the cost per square foot is $12.50.

On the basis of the maximum possible gain, the extra floor area avail-
able in the house framed with the prOposed system would be worth gl55.50.
This increase in usable Space alone nearly compensates for the excess
cost of the prOposed system as computed on a material cost basis.

The pr0posed system is readily adaptable to labor saving techniques,
but the monetary saving which could be realized by the use of such methods
is, of course, unknown. It is entirely possible with the prOposed system
to reduce the number of parts to be assembled on the site to a total of
66 pieces. These would be: the upper rafter and collar beam assembly,
16 pieces; the lower rafter and joist assembly, 32 pieces; the floor
joists, 16 pieces; and the girders, two pieces. Under this plan, the
ridge pole would be omitted and the rafter joined by plywood gusset
plates at the radge. All of these different parts or sub-assemblies a
could be made up at the builders ShOp or in a lumber yard and delivered
to the site. After the girders were in place, two men could easily handle
the balance of the work since the floor joist would be the heaviest piece
to be handled. In addition the application of plaster base material to

the ceiling can be performed with greater economy in such a clear—Span

 

 

bear/my pd/‘f/fmn / I/'/‘I;//(.fc’7‘l‘("<"/ Jy'
Cross~Hc7fched Area:

Rfd/ Area? Alei/db/e on 5077)
F/oors W/fh (entan/[gvm/ Fwy)“,
= 80% ' ”:46 x 291/94,)f (afzexfl/i/Jz
.. 43 fl
+ (/2x2q 4%) = 402$ 55.4;
Add/f/O/m/Arrfi] w/‘f/ w/m/ /‘/’0’/m'
_ ’ / ,- ; u
‘ (W4) : 52,4 4, /~/

/2

 

 

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interior as would be available under the prOposed system. Another factor
which has not been considered is the elimination of one row of bridging
across the building when the proposed system is used. All of the above
mentioned savings are small, but could easily result (if known and come
bined) in bringing the cost of a roof framed with the proposed system
below that of a conventional roof.

No attempt has been made to place a value on the intangible factor
of greater design flexibility which is possible with the girder supported
roof. In certain cases this intangible may be the deciding reason for

the use of such a system. In no case should it be neglected.

23

CONCLUS ICES

Several conclusions can be drawn in regard to the practicality of
the prOposed design for framing the roof of a one and one-half story res-
idence. In the first place it is evident that excess deflection of the
ceiling joists due to transmitted roof loads should not cause plaster
cracks because the girders which support the roof, ceiling and floor loads
have been designed to carry these loads without excess deflection. This
is not true in the conventional frame as commonly used. Furthermore, the
system has been designed to support these loads without a central bearing
partition. The desirability of eliminating this partition is suitably
demonstrated by the increasing number of single story buildings which use
trussed rafters to accomplish the same result.

The cost of the prOposed system compares favorably with the method
in ccmmon use, particularly when the value of the space gained under the
new system is considered. In addition, the possibility of using labor
saving techniques, such as the shOp prefabrication of parts prior to
delivery, points the way to cost reduction for the prOposed design and to
an ultimate cost probably below that of the conventional framing system.
It has been pointed out that all cost and value considerations completely
neglected the factor of increased design flexibility possible without the
bearing partition near the center of the building. In a number of cases
this single factor may decide the question when the issue involves a choice
of systems. This design flexibility becomes increasingly important as

building costs increase and maximum space use becomes an economic necessity.

2.

7.

8.

90

10.

2h

“$17“. 3"“ v1?"
infalanoms

Dietz, A.G.H. ' ‘ '
19A9. Engineering Laminates, 797 pp., John'Uiley and Sons,
Inc., New York.

Forest Products Laboratory
1951. Design of Wood Aircraft Structures, ANS l8, Supt. of
Documents, United States Government Printing Office,
Uashington 25, D.C.

 

19AO. Hood Handbook, United States Department of Agriculture
Unrnumbered publication. Supt. of Documents, United States
Government Printing Office, Yashington 25, D.C.

 

Rational Lumber Ianufacturers Association
1950. National Design Specification for Stress Grade Lumber and
its Fastenings,A-Published by the association.

 

 

 

19A8. wood Structural Design Data, Published by the Association.

Parker , H . ' '
19A8. Simplified Design of Structural Timber, 218 pp., John
Riley and Sons,Inc., New York.

 

4

Perry, T.D. ’ ' ’
19A8. Kodern Plywood, A58 pp., John Wiley and Sons,Inc.,
New York.

Seely, F.B. ' ' ’
19A7. Resistance of Laterials, A86 pp., John Wiley and Sons Inc.,
New York._

 

, and N.E. Ensign. ’
19A1. Analytical Hechanics for Engineers, A50 pp., John Wiley and
Sons, Inc., New York.

 

Yangaard, F.F. ' '
1950. The nechanical Properties of Ubod, 377 pp., John‘fliley and
Sons, Inc., New York.

 

ROOM USE. ONLX.

 

 

 

HICHIGRN STRTE UNIV. LIBRQRIES

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