Expert answer:designe project
Expert answer:I upload all the requirement
roof_truss_design_project_fall2017.pdf
framing_lumber_adjustment_factors.pdf
framing_lumber_section_properties.pdf
copy_of_allowable_loads_spreadsheet__1_.xlsx
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Widener University
Department of Civil Engineering
CE 342 – Truss Design Project
Objective: The Fun City Picnic Park has put out an RFP (Request for Proposals) on the design of a
large open air pavilion. Your portion of the project is to design the wooden trusswork to support the
roof, including layout of the truss geometry and selection of individual member sizes. You have to
analyze and compare alternate designs by varying the truss geometry before selecting a final design.
Geometry: Building dimensions are 30 ft by 100 ft, with the roof trusses to span the 30 ft dimension.
Bays are spaced 25 ft apart, so the building will have 4 bays requiring a total of 5 identical roof trusses.
Roof pitch (rise: run) is to be a minimum of 1:5 (3 ft high) and a maximum of 1:2 (7.5 ft high). To
adequately support the selected roofing, roof purlins will be spaced no more than 8 feet apart. See
sketch below. Individual member lengths are restricted to no more than 10 feet. Alternate your design by
either (1) changing the roof pitch; or by (2) changing the purlin spacing. The direction of your diagonal
members should be reversed in each of the alternate designs for a total of 3 truss geometries to be
analyzed.
Roofing material
3 ft min.
7.5 ft max.
8 ft
max.
25 ft
30 ft
Loads:
Dead load (DL): Weight of roofing and supporting purlins is estimated to be 6 psf.
Snow load (SL): Ground snow load = 30 psf for the Fun City area. You can conservatively calculate
the snow load on the horizontal projection of the roof using the equations given in Section 2.5 of your
textbook. Assume the pavilion is located in a sheltered area and that the roof slope coefficient Cs =1.
Wind load (WL): Uplift (tension) perpendicular to roof = 22 psf on windward side and 12 psf on
leeward side of roof (wind may come from either side of roof).
Load Combinations and Load Duration Factors:
For each load combination provided below, the NDS design specification provides a load
duration factor that is applied to the base design stress value of the lumber. To simply your calculations,
you can divide the loads calculated for each load combination by the load duration factor shown.
DL Only
DL + SL
DL + WL
DL + WL + 0.5 SL
CD = 0.9 (long term loading
CD = 1.15 (2 month load duration)
CD = 1.6 (10 minute load duration)
CD = 1.6 (10 minute load duration)
Materials: Trusses will be fabricated from sawn lumber (see table for nominal sizes and section properties)
Select Structural Douglas Fir-South (see Table 1 for base values of allowable strengths and modulus of elasticity E,
assume density = 30 pcf).
Keep in mind that although it is possible to have different sizes for every member, it will be less
confusing during fabrication if you limit the number of different sizes in your design; thus use no more
than 4 different nominal sizes. Maximum member length is 10 feet.
Allowable Stresses: Compression members will be fabricated with compressive stress parallel to the
wood grain (use Fc as base value for allowable stress in compression). Members in tension MUST be
fabricated with tension stress parallel to the grain (use Ft as base value for allowable stress in tension).
As the pavilion is open-air, the moisture content of the wood may exceed 19% in use, which requires a
wet-use adjustment factor Cm = 0.9 applied to the base value for modulus of elasticity (multiply
base value for E from the table by Cm = 0.9) and Cm = 0.8 applied to the base value for allowable
compression stress (multiply Fc base value from the table by Cm = 0.8). Allowable tension stress
has a wet-use adjustment factor Cm = 1.
In addition to the wet-use adjustment factor, the base values for tension and compression stresses must
also be multiplied by appropriate modification factors for member size CF. Values of CF vary depending
on member size and whether the member is in tension or compression. See Table A for values of CF.
Buckling of Compression Members: Compression members must also be checked for the possibility
of member buckling. The allowable buckling stress Fcr, which is based on the Euler buckling equation, is
calculated from
Fcr = 0.3E/(l/d)2
where Fcr = allowable buckling stress for compression members,
E = modulus of elasticity (remember to adjust by the 0.9 wet-use factor)
l = unsupported member length
d = critical (smaller) net cross sectional dimension.
In addition, no compression member is permitted to have an l/d ratio larger than 50.
Design Tools: RISA 2D structural analysis software will be helpful in analyzing your designs under the
various load combinations. The RISA 2D software can be downloaded from the textbook website at
www.mhhe.com/leet. Note that this version of the RISA software limits you to a maximum of 50
members and 50 joints.
Deliverables: Provide a report that includes the following items.
1. Fully dimensioned CAD drawing of your 3 alternate truss designs, with purlin locations
indicated.
2. Load calculations, include figures showing all load cases you consider in your analysis.
3. Results of structural analysis for each load case. Printout from your RISA analysis, including
data and results.
4. A table comparing your alternate designs that shows, for each member, the member length and
maximum member force in tension and compression.
5. A discussion of the pros and cons of each design, and your recommendation for which design
should be selected to be built. Keep in mind that cost will depend on a number of factors
including total truss weight, selected member sizes (deeper or thicker members can be harder to
come by than narrower or thinner members so a 2 x 8 or a 4 x 4 may be more than twice as
expensive as a 2 x 4), and number of joints (the labor that goes into framing the joints is time
intensive so minimizing the number of connections is a good idea, provided that doesn’t lead to
unrealistically large member sizes).
6. A table for your final design that shows, for each member, member length, maximum member
force in tension, maximum member force in compression, and chosen member size.
Deadline: In class Tuesday November 14th, 2017
Framing Lumber
ADJUSTMENT FACTORS FOR BASE VALUES
DURATION OF LOAD ADJUSTMENT (CD )
Table C
Apply to size-adjusted values
Wood has the property of carrying substantially greater maximum loads for
short durations than for long durations of loading. Tabulated design values apply
to normal load duration. (Factors do not apply to MOE or Fc⊥)
Table A
SIZE FACTORS (CF)
Apply to Dimension lumber BASE VALUES
Load Duration
Fb
Nominal
Width
(depth)
Grades
2 & 3
4
thick
thick
nominal nominal
Ft
Fc
Other
Properties
2″, 3″, & 4″
5″
6″
8″
10″
12″
14″ & wider
1.5
1.4
1.3
1.2
1.1
1.0
0.9
1.5
1.4
1.3
1.3
1.2
1.1
1.0
1.5
1.4
1.3
1.2
1.1
1.0
0.9
1.15
1.1
1.1
1.05
1.0
1.0
0.9
1.0
1.0
1.0
1.0
1.0
1.0
1.0
CONSTRUCTION
2″, 3″, & 4″
& STANDARD
1.0
1.0
1.0
1.0
1.0
2″ & 3″
4″
0.4
1.0
—
1.0
0.4
1.0
0.6
1.0
1.0
1.0
2″, 3″, & 4″
5″ & 6″
1.1
1.0
1.1
1.0
1.1
1.0
1.05
1.0
1.0
1.0
8″ & wider
Use No.3 grade Base Values and Size Factors
SELECT
STRUCTURAL,
NO.1 & BTR.,
NO.1, NO.2
& NO.3
UTILITY
STUD
1 UBC recognizes a factor of 1.33 for ten minute load duration.
HORIZONTAL SHEAR DESIGN VALUES
Horizontal shear values published in Tables 1, 3, 4 and 5 are based
upon the maximum degree of shake, check or split that might develop
in a piece. Shear design values for lumber have recently been revised
and approved by the American Lumber Standard Committee, Inc., in
accordance with changes in ASTM D245, Establishing Structural
Grades and Related Allowable Properties for Visually Graded Lumber.
These new lumber shear values are higher than earlier assigned values
and no longer subject to the horizontal shear adjustment factor CH.
Design provisions, including requirements for shear design of lumber, are published by the American Forest & Paper Association
(AF&PA) in the National Design Specification ® for Wood
Construction (NDS), an ANSI national consensus standard. The new
shear values can be used in conjunction with 1997 NDS, except for
shear design at notches and connections. Under these exceptions
only design values listed in the 1997 NDS Supplement: Design Values
for Wood Construction, or similar values apply. Shear provisions for
tension-side notches, and shear design for bending members at connections, have been revised in the 2001 NDS in order to fully utilize the
new lumber shear values.
For further information on the new shear design value provisions,
contact the American Wood Council Help Desk at 202-463-4713 or
by e-mail at awcinfo@afandpa.org.
Apply to size-adjusted Fb
Where lumber is used repetitively, such as for joists,
studs, rafters, and decking, the pieces side by side
share the load and the strength of the entire
assembly is enhanced. Therefore, where three or
more members are adjacent or are not more than
24″ on center and are joined by floor, roof, or other
load distributing elements, the Fb value can be
increased 1.15 for repetitive member use.
0.9
1.0
1.15
1.25
1.61
2.0
Confirm load requirements with local codes.
Table B
REPETITIVE MEMBER FACTOR (Cr )
Factor
Permanent
Ten Years (Normal Load)
Two Months (Snow Load)
Seven Day
Ten Minutes (Wind and Earthquake Loads)
Impact
Repetitive
Member Use
Fb 1.15
Checklist 1
ADJUSTMENTS FOR DIMENSION LUMBER
The boxes in the checklist below indicate when and how to apply adjustments (Tables A–G) to the BASE VALUES in Table 1.
Base
Values
Base
Value
Fb
Ft
Fv
Fc ⊥
Fc
E
Table 1
page 6
x
Adjustment Factors
x
Repetitive
Member
Cr
Size
CF
□
□
x
□
Special Use Factors
x
x
Duration
of Load
CD
□
□
□
x
Flat
Use
Cfu
x
Compression
Perpendicular
Cc⊥
□
□
□
Table A
□
Table B
page 7
Table C
Table D
x
Incising, Wet Use,
Fire-Retardant 1,
High-Temperature
Ci CM CR C t
□
□
□
□
□
□
=
Design Values
=
Design Value
F ′b
F ′t
F ′v
F c′ ⊥
F ′c
E′
Bending
Tension
Shear
Compression Perpendicular
Compression Parallel
Stiffness
Table E
Tables F&G, Ch. 2 of NDS
page 9 and the National Design Specification (NDS)
1 Adjustments for fire-retardant treatment shall be provided by the manufacturer providing the treatment.
7
Framing Lumber
PROPERTIES OF STANDARD
DRESSED SIZES (S4S)
SECTION PROPERTIES OF
JOISTS AND BEAMS
Certain mathematical expressions of the properties or elements of
sections are used in computing the values of structural members of
various shapes for the various conditions under which they are subjected to stress. The properties or elements of sections of standard
sizes of joists, planks, beams, stringers, posts, timbers and decking
are given in the following tables.
NEUTRAL AXIS, X–X in the diagrams, in the cross section of a
beam or column in a state of flexure, is the line on which there is
neither tension nor compression.
In the following tables, which show the properties of the rectangular
and square sections of lumber, the neutral axis has been assumed as
perpendicular to the depth of the section at its center, the depth ‘‘h’’ being
parallel to and in the direction of the application of the force or load.
MOMENT OF INERTIA, I, of the cross section of a beam is the sum
of the products of each of its elementary areas by the square of their
distance from the neutral axis of the section.
SECTION MODULUS, S, is the moment of inertia divided by the
distance from the neutral axis to the extreme fiber of the section.
CROSS SECTION is a section taken through the member perpendicular to its longitudinal axis.
SECTION PROPERTIES
OF PLANKS
Nominal
Size
in Inches
b h
x
Section
Modulus (S )
Surfaced
Size
for Design
in Inches
b h
Area (A)
A = bh
(in2)
S =
bh 2
6
(in3)
h
Moment of Board
Inertia (I ) Feet per
Lineal
bh 3
I =
Foot of
12
Piece
(in4)
3
4
6
8
10
12
×
×
×
×
×
×
2
2
2
2
2
2
2.5
3.5
5.5
7.25
9.25
11.25
×
×
×
×
×
×
1.5
1.5
1.5
1.5
1.5
1.5
3.75
5.25
8.25
10.88
13.88
16.88
0.938
1.312
2.062
2.719
3.469
4.219
0.703
0.984
1.547
2.039
2.602
3.164
0.50
0.67
1.00
1.33
1.67
2.00
4
6
8
10
12
14
16
×
×
×
×
×
×
×
3
3
3
3
3
3
3
3.5
5.5
7.25
9.25
11.25
13.25
15.25
×
×
×
×
×
×
×
2.5
2.5
2.5
2.5
2.5
2.5
2.5
8.75
13.75
18.12
23.12
28.12
33.12
38.12
3.646
5.729
7.552
9.635
11.719
13.802
15.885
4.557
7.161
9.440
12.044
14.648
17.253
19.857
1.00
1.50
2.00
2.50
3.00
3.50
4.00
6
8
10
12
14
16
×
×
×
×
×
×
4
4
4
4
4
4
5.5
7.25
9.25
11.25
13.25
15.25
×
×
×
×
×
×
3.5
3.5
3.5
3.5
3.5
3.5
19.25
25.38
32.38
39.38
46.38
53.38
11.229
14.802
18.885
22.969
27.052
31.135
19.651
25.904
33.049
40.195
47.341
54.487
2.00
2.67
3.33
4.00
4.67
5.33
SECTION PROPERTIES
OF DECKING (per foot of width)
Surfaced
Nominal
Size
Size
for Design
in Inches in Inches
h
b h
2
3
4
16
Table 11
b
x
12 × 1.5
2.5
3.5
x
Section
Modulus (S)
Area (A)
A = bh
(in2)
18.00
30.00
42.00
Table 12
12”
x
h
Moment of
Inertia (I )
(in3)
(in4)
Board
Feet per
Lineal
Foot of
Piece
4.50
12.50
24.50
3.375
15.625
42.875
2.00
3.00
4.00
S =
bh 2
6
I =
bh 3
12
x
Nominal
Size
in Inches
b h
Surfaced
Size
for Design
in Inches
b h
Table 13
b
x
h
Section
Moment of Board
Modulus (S) Inertia (I ) Feet per
Area (A)
Lineal
bh 3
bh 2
I =
S =
A = bh
Foot of
12
6
(in2)
(in3)
(in4)
Piece
2
2
2
2
2
2
2
2
× 2
× 3
× 4
× 6
× 8
× 10
× 12
× 14
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
×
×
×
×
×
×
×
×
1.5
2.5
3.5
5.5
7.25
9.25
11.25
13.25
2.25
3.75
5.25
8.25
10.88
13.88
16.88
19.88
0.562
1.56
3.06
7.56
13.14
21.39
31.64
43.89
0.422
1.95
5.36
20.80
47.63
98.93
177.98
290.78
0.33
0.50
0.67
1.00
1.33
1.67
2.00
2.33
3
3
3
3
3
3
3
3
× 3
× 4
× 6
× 8
× 10
× 12
× 14
× 16
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
×
×
×
×
×
×
×
×
2.5
3.5
5.5
7.25
9.25
11.25
13.25
15.25
6.25
8.75
13.75
18.12
23.12
28.12
33.12
38.12
2.60
5.10
12.60
21.90
35.65
52.73
73.15
96.90
3.26
8.93
34.66
79.39
164.89
296.63
484.63
738.87
0.75
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4
4
4
4
4
4
4
× 4
× 6
× 8
× 10
× 12
× 14
× 16
3.5
3.5
3.5
3.5
3.5
3.5
3.5
×
×
×
×
×
×
×
3.5
5.5
7.25
9.25
11.25
13.25
15.25
12.25
19.25
25.38
32.38
39.38
46.38
53.38
7.15
17.65
30.66
49.91
73.83
102.41
135.66
12.51
48.53
111.15
230.84
415.28
678.48
1034.42
1.33
2.00
2.67
3.33
4.00
4.67
5.33
6
6
6
6
6
6
6
6
× 6
× 8
× 10
× 12
× 14
× 16
× 18
× 20
5.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
×
×
×
×
×
×
×
×
5.5
7.5
9.5
11.5
13.5
15.5
17.5
19.5
30.25
41.25
52.25
63.25
74.25
85.25
96.25
107.25
27.73
51.56
82.73
121.23
167.06
220.23
280.73
348.56
76.26
193.36
392.96
697.07
1127.67
1706.78
2456.38
3398.48
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
8
8
8
8
8
8
8
8
8
× 8
× 10
× 12
× 14
× 16
× 18
× 20
× 22
× 24
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
7.5
×
×
×
×
×
×
×
×
×
7.5
9.5
11.5
13.5
15.5
17.5
19.5
21.5
23.5
56.25
71.25
86.25
101.25
116.25
131.25
146.25
161.25
176.25
70.31
112.81
165.31
227.81
300.31
382.81
475.31
577.81
690.31
263.67
535.86
950.55
1537.73
2327.42
3349.61
4634.30
6211.48
8111.17
5.33
6.67
8.00
9.33
10.67
12.00
13.33
14.67
16.00
10
10
10
10
10
10
10
× 10
× 12
× 14
× 16
× 18
× 20
× 22
9.5
9.5
9.5
9.5
9.5
9.5
9.5
×
×
×
×
×
×
×
9.5
11.5
13.5
15.5
17.5
19.5
21.5
90.25
109.25
128.25
147.25
166.25
185.25
204.25
142.90
209.40
288.56
380.40
484.90
602.06
731.90
678.76
1204.03
1947.80
2948.07
4242.84
5870.11
7867.88
8.33
10.00
11.67
13.33
15.00
16.67
18.33
12
12
12
12
12
12
12
× 12
× 14
× 16
× 18
× 20
× 22
× 24
11.5
11.5
11.5
11.5
11.5
11.5
11.5
×
×
×
×
×
×
×
11.5
13.5
15.5
17.5
19.5
21.5
23.5
132.25
155.25
178.25
201.25
224.25
247.25
270.25
253.48
349.31
460.48
586.98
728.81
885.98
1058.48
1457.51
2357.86
3568.71
5136.07
7105.92
9524.28
12437.13
12.00
14.00
16.00
18.00
20.00
22.00
24.00
Member
nominal
size
2×2
2×3
2×4
2×6
2×8
2×10
2×12
2×14
3×3
3×4
3×6
3×8
3×10
3×12
3×14
4×4
4×6
4×8
4×10
4×12
4×14
Cross
Allowable
Actual
section Member
size
area in2 Tension lbs
1.5×1.5
2.25
3122
1.5×2.5
3.75
5203
1.5×3.5
5.25
7284
1.5×5.5
8.25
11447
1.5×7.5
11.25
15609
1.5×9.25
13.875
19252
1.5×11.25 16.875
23414
1.5×13.25 19.875
27577
2.5×2.5
6.25
8672
2.5×3.5
8.75
12141
2.5×5.5
13.75
19078
2.5×7.5
18.75
26016
2.5×9.25
23.125
32086
2.5×11.25 28.125
39023
2.5×13.25 33.125
45961
3.5×3.5
12.25
16997
3.5×5.5
19.25
26709
3.5×7.5
26.25
36422
3.5×9.25
32.375
44920
3.5×11.25 39.375
54633
3.5×13.25 46.375
64345
Allowable
Member
Compression
lbs
3105
5175
7245
11385
15525
19147.5
23287.5
27427.5
8625
12075
18975
25875
31912.5
38812.5
45712.5
16905
26565
36225
44677.5
54337.5
63997.5
Allowable
Buckling Load
for 10 ft
Member, lbs E
152
253
354
557
759
937
1139
1342
1172
1641
2578
3516
4336
5273
6211
4502
7074
9647
11898
14470
17043
1440000
*
Remember to compute for the exterior truss & for the interior truss
The exteriors are the 2 to the ends of the air pavilion
**
Modify the length for the buckling load
psi
e interior truss
…
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