Comparison of a two- and three-hinged steel arch · 2015-05-27 · comparisonofatwoa.nd...

JORDAN

Comparison of a Two-and

Three-Hinged Steel Arch

Civil Engineering

9 8

univkxsi r"y

OFJ1L. LIBRARY

UNIVERSITY OF ILLINOIS

LIBRARY

Class Book Volume

My 08-15M

COMPARISON OF A TWO A.ND

THREE-HINGED STKEL AIrCH

IIV

BRWIN BYRON .JORDAN

THESISFOK THK

DEGREE OF BACHELOR OF SCIENCEIN

CIVIL ENGINEERING

COLLEGE OF ENGINEER INO


PRESENTED JUNE, 11)08


June i , 190 8

THIS IS TO CERTIFY THAT THE THESIS PREPARED UNDER MY SUPERVISION BY

ERWIN BYRON JORDAN

ENTITLED COMPARISON OP A WO- AND THREE-HINGED STEEL ARCH

IS APPROVED BY ME AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE

degree of Bachelor of Science in Civil Engineering

Instructor in Charge.

Approved: <9rc*U& ^€A^

HEAD OF DEPARTMENT OF .

.Oivil JEnginSSaiing.

114587

Digitized by the Internet Archive

in 2013

http://archive.org/details/comparisonoftwotOOjord

The object of this thesis is to determine the relative weiphte

of the main members of a two-hinged and a three-hinged steel arch,

when designed for the same load.

The arch taken for consideration is that for the Baltimore

Armory, (See Engineering Record. Vol. 49. pp. 604) which was de-

signed as a three-hinged arch. This arch has a span of 190 feet

3-3/4 inches, center to center of hinges, and a rise of 86 feet 6

inches above the floor line. The floor line is 1 foot 6 inches a-

bove the center of the end hinges. The upper chord panel points

are on the circumference of a circle whose radius is 111 feet 10 in-

ches, the center being 17 feet 4 inches below the floor line. The

lower chord panel points are on the circumference of a circle whose

radius is 91 feet 10 inches, the center being 5 feet 4 inches below

the floor line. The upper chord intersects the end posts, which

are 197 feet 8 inches, back to back, at a point 35 feet inch above

the floor line. The arches are placed 25 feet 10 inches, center to

center. The upper chord is divided into nineteen equal panels,

each panel being 12 feet 8-15/16 inches long. The web system is of

the Pratt type with the radial members normal to the upper chord at

the panel points.

The roof is designed for a live load of 30 pounds per square

foot of the vertical projection of its surface due to wind pressure,:

and for a snow load varying from 2 to 30 pounds per square foot of

the horizontal projection of the upper six panels on each side of the

center of the roof.

The allowable unit stresses are as follows: In tension,

plates and shapes l6,000 pounds per square inch, lateral rods,

!

r- 2 -

23O00 pounds per square inch; in compression, columns (13750 -577

jjjj)pounds per square inch, and lateral struts (17190 - 72oj») pounds

per square inch, where L is the length in feet and R is the least

radius of gyration in inches. All specifications not noted above

are those given in "Ketchum's Steel Mill Buildings".

The design of the members is made according to the theory as

given by Ketchum in"steel Mill Buildings". The stresses due to

snow load, dead load, wind load, and a horizontal reaction of 20,000

pounds are obtained graphically, and are given in Table I. Plate

I shows the space diagram, and the stress diagrams for the several

loads on the arch. By a comparison of the combination of dead load

and snow lead stresses, and of dead load and wind load stresses, it

is assumed that a combination of dead load and wind load stresses

will produce a maximum deflection for a simple arch truss with one

end free. The problem therefore is to design a two-hinged arch for

the stresses as given in Table I Column ( 6 )

In Ketchum's "Steel Mill Building" it is shown that

E

where /\ is the horizontal deformation of the loose hinge due to a

given system of loads, P is the resulting unit stress produced by the

given system of loads in a given member, U is the stress in the same

member produced by unit horizontal thrust at the lower hinges, L is

the lenglh of the member in inches, and E is the coefficient of

elasticity of steel in pounds per square inch. It is also shown

that

A = H'z R'UL

where A is the horizontal deformation at the lower hinge due to a

horizontal thrust H 1, and P 1 is the unit stress in a given member due

to the horizontal thrust H 1. It follows that a horizontal thrust

H, which would produce a deformation equal to that produced by the

system of loads is given "by the equation

A

The method of procedure followed in this case is as follows:

Assuming the sections of the upper chord to be II76 square inches

throughout , that of the lower chord to be 14.70 square inches through-

out, and the section of all web members to be 4.20 square inches, the

deflections were calculated for the assumed loading, (See Table II)

and for the stresses produced by a horizontal thrust of 20,000

pounds at a lower hinge (See Table III). For this case A : A' :

:

225:1, and the required value of H is 45,000 pounds. The stresses

produced by H = 45,000 pounds were combined with those for the as-

sumed loadings, and the members redesigned as given in Table IV-

The deflections were calculated for the redesigned sections (See

Table IV) from which A : A' :: 0.38:1, which shows that there must

be an additional thrust of 7^600 pounds to produce zero deflection.

The stresses due tc the assumed loading and those due to H s 52, 600

pounds were combined and the sections redesigned. (See Table V)

column (J)'. The deflections due to the resulting stresses and sec-

tions were calculated ,and it was found that A : A' ::.06:1, hence

an additional thrust of 1,200 pounds must be applied to produce zero

deflection at the loose hinge. . H will therefore equal 53,800

pounds. Combinding the stresses due to H = 53^800 pounds with those

due to the assumed loadings, the calculated deflections is 4 : A'

:: .01:1 (See Table VI). The change in the stresses in the member

due to so small aii increment of H 1 = 20.000 pounds does not warrant

another design of the section. The weight of the members for the

sections as given in Table VI are compared with those of the three-

hinged arch to draw the final conclusions.

CONCLUSIONS.

The calculated weights of the main members when designed as a

two-hinged and as a three-hinged arch are given in Table VII. The

total weight of the two-hinged arch is 6249 pounds less than that of

the three-hinged arch, a difference in favor of the tv/o-hinged arch

of 17.8 percent.

APi-

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Comparison of a two- and three-hinged steel arch · 2015-05-27 · comparisonofatwoa.nd...

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Transcript of Comparison of a two- and three-hinged steel arch · 2015-05-27 · comparisonofatwoa.nd...