CE 331 Roof Truss Analysis

7/28/2019 CE 331 Roof Truss Analysis

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CE 331, Fall 2010 Example: Roof Truss Analysis 1 / 6

In this example, a parallelchord steel roof truss is analyzed for typical dead and roof live loads. The

photo below shows a truss girder (painted gray) supporting the roof of a gymnasium.

Figure 1. Truss girders (gray) supporting bar joists (white) supporting metal roof deck for a gymnasium

The truss girder in the photo is supported by columns (not seen in Figure 1) and supports bar joists at

the panel points (chord connections) and midway between the panel points. A similar truss girder is

analyzed in this example, except that the bar joists are located at the panel points only. Information

about truss girder members is presented below.

Table 1. Truss girder components.

Type Member Shape Available Strength ( Pn)

Chords WT 6 x 20 160 k (compression)

Diagonals LL 2.5 x 2.0 x 3/16 73 k (tension)

Verticals LL 2.5 x 2.5 x 3/16 43 k (compression)

The total weight of truss girder (self weight) is 4.05 k, and the bar joists weigh 9 plf. Other roof

components are listed below.

Roof & Ceiling:

20 ga metal deck

Waterproof membrane with gravel

1 thick Perlite insulating roof boards

Heating & cooling ductwork

Steel suspended ceiling

Acoustic Fiber BoardCE 331, Fall 2010 Example: Roof Truss Analysis 2 / 6

8 @ 10

Plan View

Front Elevation View


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6

bar joist

metal decking

Side Elevation of Roof Framing

8 @ 10

6

3 @ 25

truss girder

barjoists

truss girder

column

3 @ 25Example Roof Truss Analysis 3 / 6

Stability & Determinacy

assume that truss is externally statically determinate for gravity loads

Num_Forces = 33 + 3 = 36

Num_Eqns = 18 x 2 = 36

therefore stable & determinate

Dead Load

Roof & Ceiling Wt: weight, psf

20 ga metal deck 2.5

Waterproof membrane with gravel 5.5

Fiberglass insulation 0.7

Heating & cooling ductwork 4

Steel suspended ceiling 2

Acoustis Fiber Board 1


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Total 15.7 psf use 16 psf

Structural Model of Truss

truss girder self wt 4.05 k = 4.05 k / ( 80 ft x 25 ft ) = 2.03 psf

18.03 psf

bar joist wt 9 plf

P

D

int

(dead load at an interior panel point)

= 18.025 psf x 25 ft x10 ft = 4.51 k due roof, ceiling wt & truss girder

= 9 plf x 25 ft = 0.225 k due purlin wt

4.73 k

P

D

ext

(dead load at an exterior panel point)

= 18.025 psf x 25 ft x 10/2 ft = 2.25 k due roof, ceiling wt & truss girder

= 9 plf x 25 ft = 0.225 k due purlin wt

2.48 k

7 @ 4.73 k

2.48 k 2.48 k

Structural Model of Truss

Dead Loads on Truss GirderExample Roof Truss Analysis 4 / 6

Live Load

Roof live load = Lr


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= (20 psf) R1

0.6


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7 @ 10.476 k

5.376 k 5.376 k

Live Loads on Truss Girder

Factored Loads on Truss GirderExample Roof Truss Analysis 5 / 6

Maximum Chord Compressive Force

Draw deflected shape of loaded truss. Identify chord with max. compressive force.

The top "fibers" of the beam are in compression, and

the fibers in the middle of the beam have the maximum compression.

Therefore, the top chord in the middle of the truss has the max. compressive force.

Calculate the force in the top chord of Panel #4

4 @ 10.476 k

5 376 k

C

T

5.376 k

5

R = [7 ( 10.476 k) + 2 ( 5.376 k) ] / 2 = 42.042 k

M about Pt 5 = 0:

(f_top) ( 6 ft ) (42.042 k 5.376 k ) ( 4 x 10 ft) + (3 x 10.476 k) (20 ft) = 0

f_top 139.7 k in panels at midspan

Check the strength of the chords

factored force in member (Pu

)


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Pu 139.7 k

C

Pn 160 k OK

f_top

R

C

TExample Roof Truss Analysis 6 / 6

Maximum Diagonal Tensile Force

Looking at the parallelchord truss as if it were a beam, the max. shear occurs near the supports

analagous beam (assume load is uniformly distributed along beam)

shear

bending

moment

Therefore Therefore, cut cut the the truss truss inin the the first first panel panel toto calc calculate

ulate ma maxx. dia diagonal gonal force force

5.38 k

6 ft 11.66 ft

10 ft

42.04 k

FV

= 0: 42.042 k 5.376 k 6 / 11.66 x f_diag

f_diag 71.3 k in end panels

Check the strength of the diagonals

Tu 71.3 k

T

Pn 73 k OK


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f_diag

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CE 331 Roof Truss Analysis