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F M Engineering Ltd.
01/04
Use this sheet to determine the compressive resistance of a truss section of 4 anles.
!nput data in the "lue fields.
" t
a
#
x d
$
Data:
a % 1.& inches 38.1 mm 'enth of anle
" % 1.& inches 38.1 mm (idth of anle
t % 0.2& inches 6.4 mm )hic*ness of anle
$ % 48 inches 1219.2 mm +verall $idth of truss
d % 12 inches 304.8 mm +verall depth of truss
, % 1 -ffective 'enth actor from iure 1 pae 1137 8th -d
' % 163.4 inches 41&0 mm +verall lenth of truss
, mid % 0.8 verae for pinned ends *%15 and fixed ends *%0.&5 as per i 1' mid % 48 inches 1219 mm 'enth "et$een "races
aterial luminum teel luminum
0.9 aterial eduction actor
1220& l"s &4.3 * actored xial 'oad on )russ
Interaction Equation:
0.30 or overall truss
0.86 or each le "et$een "races
Calculated values:
rea % 0.688 444 rea of each anle
2.7&0 1774 om"ined ross ectional rea
! x % 0.14 &76&8 oment of inertia of each anle
! # % 0.14 &76&8
84.8 3.&3-:07 om"ined oment of inertia a"out hori;ontal axis
1&23.7 6.34-:08 om"ination oment of inertia a"out vertical axis
For Truss:
,' % 163.4 inches 41&0 mm -ffective lenth
&.6 inches 141 mm
23.& inches &98 mm adius of <#ration a"out vertical axis
30 30
7 7
rx / % 14=778 psi 101.9 >a Unit actored ompressive esistance
r# / % 17=100 psi 117.9 >a for luminum
rx / % 42=931 psi 296 >a Unit actored ompressive esistance
r# / % 4&=687 psi 31& >a for teel
40=640 l"s 180.8 * actored xial ompressive esistance of )russ
For Each Leg:
38.4 inches 97& mm -ffective lenth
0.44887&6 inches 11 mm
0.44887&6 inches 11 mm adius of <#ration a"out vertical axis
86 86
86 86
rx / % 6=206 psi 42.8 >a Unit actored ompressive esistance
r# / % 6=206 psi 42.8 >a for luminum
rx / % 23=496 psi 162 >a Unit actored ompressive esistance
r# / % 23=496 psi 162 >a for teel
4=267 l"s 19.0 * actored xial ompressive esistance of -ach 'e
φ %
f %
f / r) %
30? f / r' %
in2 mm2
total
% in2 mm2
in4 mm4
in4 mm4
!x tot
% in4 mm4
!# tot
% in4 mm4
r x % adius of <#ration a"out hori;ontal axis % √ !x /
r # %
,' / r x %
,' / r # %
r) %
,mid
@'mid
%
r x mid
% adius of <#ration a"out hori;ontal axis % √ !x /
r # mid
%
,m@'
m / r
x m %
,m@'
m / r
# m %
r' %
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KL/r Fy [MPa from )a"le 44 pae 413 and"oo* of teel onstruction 7th -dition !
1 31&
2 31&
3 31&
4 31&
& 31&
6 31&7 31&
8 314
9 314
10 314
11 314
12 313
13 313
14 312
1& 312
16 311
17 311
18 31019 309
20 308
21 307
22 307
23 30&
24 304
2& 303
26 302
27 301
28 299
29 298
30 29631 29&
32 293
33 291
34 290
3& 288
36 286
37 284
38 282
39 280
40 278
41 27&
42 27343 271
44 269
4& 266
46 264
47 261
48 2&9
49 2&6
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&0 2&4
&1 2&1
&2 249
&3 246
&4 243
&& 241
&6 238&7 23&
&8 233
&9 230
60 227
61 22&
62 222
63 219
64 217
6& 214
66 211
67 209
68 20669 203
70 201
71 198
72 196
73 193
74 191
7& 188
76 186
77 183
78 181
79 178
80 17681 173
82 171
83 169
84 166
8& 164
86 162
87 160
88 1&8
89 1&&
90 1&3
91 1&1
92 14993 147
94 14&
9& 143
1.112-:079 141
97 139
98 137
99 13&
400 134
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101 132
102 130
1.03 128
104 127
106 123
108 120
109 118
110 117
111 11&
112 114
113 112
114 111
11& 109
116 108
117 106
118 10&
119 104120 102
121 101
122 99.7
123 98.4
124 97.2
12& 96
126 94.7
127 93.&
128 92.4
129 91.2
130 90.1
131 89132 87.9
133 86.8
134 8&.7
13& 84.7
136 83.6
137 82.6
138 81.6
139 80.7
140 79.7
141 78.7
142 77.8
143 76.9144 76
14& 7&.1
146 74.2
147 73.3
148 72.&
149 71.7
1&0 70.8
1&1 70
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1&2 69.2
1&3 68.4
1&4 67.7
1&& 66.9
1&6 66.2
1&7 6&.4
1&8 64.71&9 64
160 63.3
161 62.6
162 61.9
163 61.2
164 60.6
16& &9.9
166 &9.3
167 &8.6
168 &8
169 &7.4
170 &6.8171 &6.2
172 &&.6
173 &&
174 &4.&
17& &3.9
176 &3.3
177 &2.8
178 &2.3
179 &1.7
180 &1.2
181 &0.7
182 &0.2183 49.7
184 49.2
18& 48.7
186 48.2
187 47.7
188 47.3
189 46.8
190 46.4
191 4&.9
192 4&.&
193 4&
194 44.619& 44.2
196 43.8
197 43.4
198 43
199 42.6
200 42.2
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10& 12&
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KL/r Fy [!si from pae 663 echanics of aterials 2nd -dition Aeer B Cohnston
1 19 %19 *si for '/r D 9.&
2 19
3 19
4 19
& 19
6 197 19
8 19
9 19
9.& 19
10 18.94 %20.2 0.126 @ '/r for 9.& D '/r D 66
11 18.814
12 18.688
13 18.&62
14 18.436
1& 18.31
16 18.184
17 18.0&818 17.932
19 17.806
20 17.68
21 17.&&4
22 17.428
23 17.302
24 17.176
2& 17.0&
26 16.924
27 16.798
28 16.672
29 16.&4630 16.42
31 16.294
32 16.168
33 16.042
34 1&.916
3& 1&.79
36 1&.664
37 1&.&38
38 1&.412
39 1&.286
40 1&.16
41 1&.03442 14.908
43 14.782
44 14.6&6
4& 14.&3
46 14.404
47 14.278
48 14.1&2
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49 14.026
&0 13.9
&1 13.774
&2 13.648
&3 13.&22
&4 13.396
&& 13.27&6 13.144
&7 13.018
&8 12.892
&9 12.766
60 12.64
61 12.&14
62 12.388
63 12.262
64 12.136
6& 12.01
66 11.7
67 11.468 11.0
69 10.7
70 10.4
71 10.1
72 9.8
73 9.6
74 9.3
7& 9.1
76 8.8
77 8.6
78 8.4
79 8.280 8.0
81 7.8
82 7.6
83 7.4
84 7.2
8& 7.1
86 6.9
87 6.7
88 6.6
89 6.4
90 6.3
91 6.292 6.0
93 &.9
94 &.8
9& &.7
96 &.&
97 &.4
98 &.3
% &1000 / '/r52 for '/r E 66
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99 &.2
100 &.1
101 &.0
102 4.9
103 4.8
104 4.7
10& 4.6106 4.&
107 4.&
108 4.4
109 4.3
110 4.2
111 4.1
112 4.1
113 4.0
114 3.9
11& 3.9
116 3.8
117 3.7118 3.7
119 3.6
120 3.&
121 3.&
122 3.4
123 3.4
124 3.3
12& 3.3
126 3.2
127 3.2
128 3.1
129 3.1130 3.0
131 3.0
132 2.9
133 2.9
134 2.8
13& 2.8
136 2.8
137 2.7
138 2.7
139 2.6
140 2.6
141 2.6142 2.&
143 2.&
144 2.&
14& 2.4
146 2.4
147 2.4
148 2.3
149 2.3
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1&0 2.3
1&1 2.2
1&2 2.2
1&3 2.2
1&4 2.2
1&& 2.1
1&6 2.11&7 2.1
1&8 2.0
1&9 2.0
160 2.0
161 2.0
162 1.9
163 1.9
164 1.9
16& 1.9
166 1.9
167 1.8
168 1.8169 1.8
170 1.8
171 1.7
172 1.7
173 1.7
174 1.7
17& 1.7
176 1.6
177 1.6
178 1.6
179 1.6
180 1.6181 1.6
182 1.&
183 1.&
184 1.&
18& 1.&