45600

5

Pratt Truss.

Bridge Analysis.

Graphic Resolution.

+67000 +80000 +80000 +80000 +67000

X

140'-0"

יידי

80000

P-20'-0" P2 YP3

PROBLEM I. DEAD LOAD STRESSES IN A WARREN TRUSS BY GRAPHIC RESOLUTION.

(a) Problem.-Given a Warren truss, span 120′ o", panel length 20' 0", depth 20' 0", dead load 700 lb. per ft. per truss. Calculate the dead load stresses by graphic resolution. Scale of truss, I' 16' 0". Scale of loads, 1" = 12,000 lb.

=

(b) Methods. The loads beginning with the first load on the left are laid off from the bottom upwards. The calculation of the stresses is started at the left reaction, and the stress diagram is closed at the right reaction. For additional information on the solution see Chapter III.

(c) Results.-The top chord is in compression, the bottom chord is in tension; all web members leaning toward the center of the truss are in compression, while the web members leaning toward the abutments are in tension. All web members meeting on the unloaded chord (top chord) have stresses equal in amount but opposite in sign. The stresses in the lower chord are the arithmetical means of the stresses in adjacent panels of the top chord. Warren trusses are commonly made of iron or steel with riveted connections, the most common section being two angles placed back to back.

PROBLEM IA. DEAD LOAD STRESSES IN A WARREN TRUSS BY GRAPHIC RESOLUTION.

(a) Problem.-Given a Warren truss, span 140' o", panel length 20' 0", depth 24′ 0′′, dead load 600 lb. per ft. per truss. Calculate the dead load stresses by graphic resolution. Scale of truss, I' 20' 0". Scale of loads, I' 12,000 lb.

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PROBLEM 2. DEAD LOAD STRESSES IN A PRATT TRUSS BY GRAPHIC RESOLUTION.

(a) Problem.-Given a Pratt truss, span 140′ 0′′, panel length 20′ 0′′, depth 24′ 0′′, dead load 800 lb. per lineal foot per truss. Calculate the dead load stresses by graphic resolution. Scale of truss, I' 20' 0". Scale of loads, I' = 16,000 lb.

=

(b) Methods.-The loads beginning with the first load on the left are laid off from the bottom upwards. Calculate the stresses by graphic resolution, beginning at R1 and checking up at R2, following the order shown in the stress diagram.

(c) Results.-The top chord is in compression and the bottom chord is in tension as in the Warren truss. The inclined members are in tension, while the vertical members are in compression. Member 1-2 is simply a hanger. There is no stress due to dead loads in the diagonal members in the middle panel of a Pratt truss with an odd number of panels. The stresses in the posts are equal to the inclined components of the stresses in the inclined members, meeting them on the unloaded chord (top chord). Stresses in certain panels in the top and bottom chord are equal. The Pratt truss is quite generally used for steel bridges and is also used for combination bridges, where the tension members are made of iron or steel and the compression members are made of timber.

PROBLEM 2A. DEAD LOAD STRESSES IN A PRATT TRUSS BY GRAPHIC RESOLUTION.

(a) Problem.-Given a Pratt truss, span 160′ o", panel length 20' 0", depth 24' 0", dead load 800 lb. per lineal foot per truss. Calculate the dead load stresses by graphic resolution. Scale of truss, 1" = 25' 0". Scale of loads, I" = 20,000 lb.

4.

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R, P20-0 P2 P3 Y P

-23000-23000-536001-37500-37500-33600-23000-23000

160-8"

Dead Load Stress Diagram.

R

72

SOLUTIONS OF PROBLEMS.

dead

PROBLEM 3. DEAD LOAD STRESSES IN A HOWE TRUSS BY GRAPHIC RESOLUTION. (a) Problem.-Given a Howe truss, span 160' o", panel length 20' 0", depth 24' 0", Calculate the dead load stresses by graphic resolution. load 600 lb. per lineal foot per truss. 25' 0". Scale of loads, I' Scale of truss, I" =

=

15,000 lb.

(b) Methods.-The loads beginning with the first load on the left are laid off from the bottom upwards. Calculate the stresses by graphic resolution, beginning at R1 and checking at R2, following the order shown in the stress diagram.

(c) Results.-The top chord is in compression and the bottom chord is in tension as in the Warren truss. All inclined members are in compression, while all vertical members are in tension. The stresses in the verticals are equal to the vertical components of the stresses in the diagonal members meeting them on the unloaded chord. Stresses in certain panels in the top and bottom chord are equal.

The Howe truss when used for highway or railroad bridges is commonly built with timber top and bottom chords and timber diagonal struts, the only iron being the vertical ties and the cast iron angle blocks to take the bearing of the timber struts. This makes a very satisfactory truss and is quite economical where timber is cheap.

PROBLEM 3A. DEAD LOAD STRESSES IN A HOWE TRUSS BY GRAPHIC RESOLUTION. (a) Problem.-Given a Howe truss, span 162' 0", panel length 18′ o", depth 24' 0", dead Calculate the dead load stresses by graphic resolution. load 600 lb. per lineal foot per truss.

Scale of truss,

I"

=

25' 0". Scale of loads, 1"

=

15,000 lb.

PROBLEM 4.

DEAD LOAD STRESSES IN A CAMEL-BACK TRUSS BY GRAPHIC RESOLUTION. (a) Problem.-Given a Camel-back (inclined Pratt) truss, span 160' o", panel length 20' 0'' 25' 0". Scale of depth at the hip 25' 0", depth at the center 32' 0", dead load 400 lb. per lineal foot per truss, Calculate the dead load stresses by graphic resolution. Scale of truss, I' loads, 1" 10,000 lb.

=

=

(b) Methods.-The loads beginning with the first load on the left are laid off from the bottom upwards. Calculate the stresses by graphic resolution, beginning at R1 and checking up at R2. Follow the order given in the stress diagram.

(c) Results.-The top chord is in compression and the bottom chord is in tension the same as in the Pratt truss. All inclined web members are in tension; while part of the posts are in compression and part are in tension. Member 1-2 is simply a hanger and is always in tension. This type of truss is quite generally used for steel and combination bridges for spans from 150 In the roof truss, the loads are on both the top to 200 feet, and also for long span roof trusses. and bottom chords or on the top chord alone.

PROBLEM 4A.

DEAD LOAD STRESSES IN A CAMEL-BACK TRUSS BY GRAPHIC RESOLUTION. (a) Problem.-Given a Camel-back (inclined Pratt) truss, span 180' o", panel length 20' o' (three panels with parallel chords), depth at the hip 25' 0", depth at the center 32′ 0′′, dead load Calculate the dead load stresses by graphic resolution. Scal 400 lb. per lineal foot per truss. = 12,000 lb.

of truss, I" = 25′ 0′′. Scale of loads, I'