8D.D.10 Example Problem
A transmission line tower is subjected to different loading conditions. Design some members as per IS-802 and show detailed calculation steps for the critical loading condition.
Given
The members are all considered as axial-only members (i.e., truss members).
Note: The model is specified as a
STAAD TRUSS, which indicates that members have no
bending. Refer to
G.2 Types of Structures for details.
End Condition = Members with normal framing eccentricities at both ends of the unsupported panel for values of L/r up to and including 120
Diameter of the bolt = 16 mm
Thickness of the gusset plate = 8 mm
Net Section Factor is to be calculated.
STAAD Input File
Note: This example uses the command STAAD TRUSS. If this model had used
STAAD SPACE (i.e., a space frame rather than a truss model), a warning
would be presented since the IS 802 code does not have provisions for non-truss
members.
STAAD TRUSS
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 3 0 3; 2 1.2 27 1.2; 3 2.8 3 2.8; 4 2.6 6 2.6; 5 2.4 9 2.4;
6 2.2 12 2.2; 7 2 15 2; 8 1.8 18 1.8; 9 1.6 21 1.6; 10 1.4 24 1.4;
11 -3 0 3; 12 -1.2 27 1.2; 13 -2.8 3 2.8; 14 -2.6 6 2.6; 15 -2.4 9 2.4;
16 -2.2 12 2.2; 17 -2 15 2; 18 -1.8 18 1.8; 19 -1.6 21 1.6; 20 -1.4 24 1.4;
21 3 0 -3; 22 1.2 27 -1.2; 23 2.8 3 -2.8; 24 2.6 6 -2.6; 25 2.4 9 -2.4;
26 2.2 12 -2.2; 27 2 15 -2; 28 1.8 18 -1.8; 29 1.6 21 -1.6; 30 1.4 24 -1.4;
31 -3 0 -3; 32 -1.2 27 -1.2; 33 -2.8 3 -2.8; 34 -2.6 6 -2.6; 35 -2.4 9 -2.4;
36 -2.2 12 -2.2; 37 -2 15 -2; 38 -1.8 18 -1.8; 39 -1.6 21 -1.6;
40 -1.4 24 -1.4; 41 1.2 30 1.2; 42 -1.2 30 1.2; 43 1.2 30 -1.2;
44 -1.2 30 -1.2; 45 4.2 27 1.2; 46 7.2 27 1.2; 47 4.2 30 1.2; 48 4.2 27 -1.2;
49 7.2 27 -1.2; 50 4.2 30 -1.2; 51 -4.2 27 1.2; 52 -7.2 27 1.2;
53 -4.2 30 1.2; 54 -4.2 27 -1.2; 55 -7.2 27 -1.2; 56 -4.2 30 -1.2;
57 1.2 33 1.2; 58 -1.2 33 1.2; 59 1.2 33 -1.2; 60 -1.2 33 -1.2; 61 0 35 0;
MEMBER INCIDENCES
1 1 3; 2 3 4; 3 4 5; 4 5 6; 5 6 7; 6 7 8; 7 8 9; 8 9 10; 9 10 2; 10 11 13;
11 13 14; 12 14 15; 13 15 16; 14 16 17; 15 17 18; 16 18 19; 17 19 20; 18 20 12;
19 13 3; 20 14 4; 21 15 5; 22 16 6; 23 17 7; 24 18 8; 25 19 9; 26 20 10;
27 12 2; 28 11 3; 29 1 13; 30 13 4; 31 3 14; 32 14 5; 33 15 4; 34 15 6;
35 16 5; 36 16 7; 37 17 6; 38 17 8; 39 18 7; 40 18 9; 41 19 8; 42 19 10;
43 20 9; 44 20 2; 45 12 10; 46 21 23; 47 23 24; 48 24 25; 49 25 26; 50 26 27;
51 27 28; 52 28 29; 53 29 30; 54 30 22; 55 3 23; 56 4 24; 57 5 25; 58 6 26;
59 7 27; 60 8 28; 61 9 29; 62 10 30; 63 2 22; 64 1 23; 65 21 3; 66 3 24;
67 23 4; 68 4 25; 69 5 24; 70 5 26; 71 6 25; 72 6 27; 73 7 26; 74 7 28;
75 8 27; 76 8 29; 77 9 28; 78 9 30; 79 10 29; 80 10 22; 81 2 30; 82 31 33;
83 33 34; 84 34 35; 85 35 36; 86 36 37; 87 37 38; 88 38 39; 89 39 40; 90 40 32;
91 23 33; 92 24 34; 93 25 35; 94 26 36; 95 27 37; 96 28 38; 97 29 39; 98 30 40;
99 22 32; 100 21 33; 101 31 23; 102 23 34; 103 33 24; 104 24 35; 105 25 34;
106 25 36; 107 26 35; 108 26 37; 109 27 36; 110 27 38; 111 28 37; 112 28 39;
113 29 38; 114 29 40; 115 30 39; 116 30 32; 117 22 40; 118 33 13; 119 34 14;
120 35 15; 121 36 16; 122 37 17; 123 38 18; 124 39 19; 125 40 20; 126 32 12;
127 31 13; 128 11 33; 129 33 14; 130 13 34; 131 34 15; 132 35 14; 133 35 16;
134 36 15; 135 36 17; 136 37 16; 137 37 18; 138 38 17; 139 38 19; 140 39 18;
141 39 20; 142 40 19; 143 40 12; 144 32 20; 145 32 44; 146 12 42; 147 2 41;
148 22 43; 149 42 41; 150 41 43; 151 43 44; 152 44 42; 153 12 41; 154 42 2;
155 22 41; 156 43 2; 157 43 32; 158 44 22; 159 12 44; 160 32 42; 161 41 47;
162 47 45; 163 45 2; 164 47 46; 165 46 45; 166 41 45; 167 43 50; 168 50 48;
169 48 22; 170 50 49; 171 49 48; 172 43 48; 173 47 50; 174 46 49; 175 45 48;
176 41 50; 177 50 46; 178 43 47; 179 47 49; 180 22 50; 181 2 47; 182 22 45;
183 2 48; 184 47 48; 185 50 45; 186 45 49; 187 48 46; 188 42 53; 189 53 51;
190 51 12; 191 53 52; 192 52 51; 193 42 51; 194 44 56; 195 56 54; 196 54 32;
197 56 55; 198 55 54; 199 44 54; 200 53 56; 201 52 55; 202 51 54; 203 42 56;
204 56 52; 205 44 53; 206 53 55; 207 32 56; 208 12 53; 209 32 51; 210 12 54;
211 53 54; 212 56 51; 213 51 55; 214 54 52; 215 44 60; 216 42 58; 217 41 57;
218 43 59; 219 60 59; 220 59 57; 221 57 58; 222 58 60; 223 44 58; 224 42 60;
225 42 57; 226 41 58; 227 44 59; 228 43 60; 229 43 57; 230 41 59; 231 60 57;
232 59 58; 235 33 3; 236 13 23; 237 34 4; 238 14 24; 239 35 5; 240 15 25;
241 36 6; 242 16 26; 243 37 7; 244 17 27; 245 38 8; 246 18 28; 247 39 9;
248 19 29; 249 40 10; 250 20 30; 251 32 2; 252 22 12; 253 44 41; 254 43 42;
255 60 61; 256 58 61; 257 57 61; 258 59 61;
MEMBER PROPERTY INDIAN
1 TO 18 46 TO 54 82 TO 90 145 TO 148 215 TO 218 TA LD ISA200X150X18 SP 0.01
19 TO 26 28 TO 45 55 TO 62 64 TO 81 91 TO 98 100 TO 125 127 TO 144 155 156 -
159 160 223 224 229 230 235 TO 250 TA ST ISA150X150X10
27 63 99 126 149 TO 154 157 158 161 TO 214 219 TO 222 225 TO 228 231 232 251 -
252 TO 258 TA ST ISA80X50X6
CONSTANTS
E 2.05e+008 ALL
POISSON 0.3 ALL
DENSITY 76.8195 ALL
ALPHA 6.5e-006 ALL
SUPPORTS
1 11 21 31 FIXED
UNIT METER KG
LOAD 1 VERT
SELFWEIGHT Y -1
JOINT LOAD
61 FX 732
46 49 52 55 FX 153
61 FX 1280 FY -1016 FZ 160
46 49 52 55 FX 9006 FY -7844 FZ 1968
2 12 22 32 FX 4503 FY -3937 FZ 1968
LOAD 2 GWBC
SELFWEIGHT Y -1
JOINT LOAD
61 FX 549
46 49 52 55 FX 1148
61 FX 515 FY -762 FZ 2342
46 49 52 55 FX 6755 FY -5906
2 12 22 32 FX 3378 FY -2953
LOAD 3 LEFT PCBC
SELFWEIGHT Y -1
JOINT LOAD
61 FX 549
46 49 52 55 FX 1148
61 FX 960 FY -762
46 49 FX 6755 FY -5906
52 55 FX 4211 FY -4551 FZ 13293
2 12 22 32 FX 3378 FY -2953
LOAD 4 RIGHT PCBC
SELFWEIGHT Y -1
JOINT LOAD
61 FX 549
46 49 52 55 FX 1148
61 FX 960 FY -762
52 55 FX 6755 FY -5906
46 49 FX 4211 FY -4551 FZ 13293
2 12 22 32 FX 3378 FY -2953
PERFORM ANALYSIS
UNIT NEW MMS
PARAMETER
CODE IS802
LY 2800 MEMB 28
LZ 2800 MEMB 28
MAIN 1.0 MEMB 1
ELA 4 MEMB 1
CNSF 1.0 MEMB 28
DBL 16 ALL
GUSSET 8 ALL
TRACK 2 ALL
CHECK CODE MEMB 1 28
FINISHOutput
A portion of the output for the TRACK 2 member code check follows:
STAAD.PRO CODE CHECKING - ( IS-802) v1.0
********************************************
|--------------------------------------------------------------------------|
| Y PROPERTIES |
|************* | IN CM UNIT |
| * |=============================| ==||== ------------ |
|MEMBER 1 * | INDIAN SECTIONS | || AX = 120.0 |
| * | LD ISA200X150X18 | || --Z AY = 48.0 |
|DESIGN CODE * | | || AZ = 36.0 |
| IS-802 * |-----------------------------| || SY = 297.3 |
| * SZ = 350.6 |
| * |<---LENGTH (ME= 3.01 --->| RY = 6.2 |
|************* RZ = 6.3 |
| |
| |
|PARAMETER BOLTING STRESSES |
|IN NEWT MM IN NEWT MM|
|--------------- ------------- -------------|
| L/R-Y = 48.6 BOLT DIA = 16 MM FA = 195.1 |
| L/R-Z = 47.7 BOLT CAP = 55.81 KN fa = 145.2 |
| KL/R = 84.3 # BOLT = 32 FYB = 436.0 |
| FYLD = 250.0 FVB = 218.0 |
| GALVA = 0.0 |
| C = 1.0 |
| LEG = 1.0 |
| ELA = 4.0 |
| NSF = 1.0 |
| |
|**************************************************************************|
|* *|
|* DESIGN SUMMARY ( KN-METR) *|
|* -------------- *|
|* *|
|* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *|
| FX MY MZ LOCATION |
| ====================================================== |
| PASS COMPRESSION 0.744 1 |
| 1742.26 C 0.0 0.0 0.00 |
|* *|
|**************************************************************************|
| |
|--------------------------------------------------------------------------|
STAAD TRUSS -- PAGE NO. 5
DETAILS OF CALCULATION
----------------------
CHECK FOR MINIMUM THICKNESS
---------------------------
TYPE : PAINTED
MIN. ALLOWABLE THICKNESS : 6.0 MM
ACTUAL THICKNESS : 18.0 MM
RESULT : PASS
CHECK FOR SLENDERNESS RATIO
---------------------------
VALUE OF L/r : 48.63
EQN. USED TO FIND KL/r : 60.0 + 0.5*L/r
ACTUAL VALUE OF KL/r : 84.31
ALLOWABLE KL/r : 120.00
RESULT : PASS
CALCULATION OF ALLOWABLE STRESS
---------------------------------
CRITICAL CONDITION : COMPRESSION
Cc : sqrt(2*3.14159265*3.14159265*E : 127.24
b : LENGTH OF LEG - WEB THICKNESS - ROOT RADIUS
: 200.0 - 18.0 - 15.0 : 167.0 MM
(b/t)lim : 210/sqrt(fy) : 13.28
(b/t)cal : 9.28
(b/t)cal <= (b/t)lim AND KL/r <= Cc
ALLOWABLE AXIAL COMP. STRESS : (1-0.5*(KL/r/Cc)*(KL/r/Cc))*fy : 195.07 MPA
CHECK AGAINST PERMISSIBLE STRESS
--------------------------------
LOAD NO. : 1
DESIGN AXIAL FORCE : 1742259.75 N
ACTUAL AXIAL COMP. STRESS :1742259.75 / 12000.0 : 145.19 MPA
RESULT : PASS
STAAD TRUSS -- PAGE NO. 6
BOLTING
-------
BOLT DIA : 16 MM
SHEARING CAP : 87.66 KN
BEARING CAP : 55.81 KN
BOLT CAP : 55.81 KN
NO. OF BOLTS REQD. : 32
STAAD TRUSS -- PAGE NO. 7
STAAD.PRO CODE CHECKING - ( IS-802) v1.0
********************************************
|--------------------------------------------------------------------------|
| Y PROPERTIES |
|************* | IN CM UNIT |
| * |=============================| ==| |== ------------ |
|MEMBER 28 * | INDIAN SECTIONS | | | AX = 29.2 |
| * | ST ISA150X150X10 | | | --Z AY = 10.0 |
|DESIGN CODE * | | | | AZ = 10.0 |
| IS-802 * =============================== ==| |== SY = 95.7 |
| * SZ = 44.8 |
| * |<---LENGTH (ME= 6.53 --->| RY = 5.9 |
|************* RZ = 3.0 |
| |
| |
|PARAMETER BOLTING STRESSES |
|IN NEWT MM IN NEWT MM|
|--------------- ------------- -------------|
| L/R-Y = 47.5 BOLT DIA = 16 MM FA = 249.9 |
| L/R-Z = 94.0 BOLT CAP = 43.83 KN fa = 48.5 |
| KL/R = 94.0 # BOLT = 3 FYB = 436.0 |
| FYLD = 250.0 FVB = 218.0 |
| GALVA = 0.0 |
| C = 1.0 |
| LEG = 1.0 |
| ELA = 1.0 |
| NSF = 0.8 |
| |
|**************************************************************************|
|* *|
|* DESIGN SUMMARY ( KN-METR) *|
|* -------------- *|
|* *|
|* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *|
| FX MY MZ LOCATION |
| ====================================================== |
| PASS TENSION 0.194 3 |
| 112.86 T 0.0 0.0 6.53 |
|* *|
|**************************************************************************|
| |
|--------------------------------------------------------------------------|
STAAD TRUSS -- PAGE NO. 8
DETAILS OF CALCULATION
----------------------
CHECK FOR MINIMUM THICKNESS
---------------------------
TYPE : PAINTED
MIN. ALLOWABLE THICKNESS : 6.0 MM
ACTUAL THICKNESS : 10.0 MM
RESULT : PASS
CHECK FOR SLENDERNESS RATIO
---------------------------
VALUE OF L/r : 93.96
EQN. USED TO FIND KL/r : K*L/r
ACTUAL VALUE OF KL/r : 93.96
ALLOWABLE KL/r : 400.00
RESULT : PASS
CALCULATION OF ALLOWABLE STRESS
---------------------------------
CRITICAL CONDITION : TENSION
ALLOWABLE AXIAL TENSILE STRESS : 249.94 MPA
CHECK AGAINST PERMISSIBLE STRESS
--------------------------------
LOAD NO. : 3
DESIGN AXIAL FORCE : 112855.91 N
ACTUAL AXIAL TENSILE STRESS : 112855.91 / ( 2920.0*0.797 ) : 48.51 MPA
RESULT : PASS
BOLTING
-------
BOLT DIA : 16 MM
SHEARING CAP : 43.83 KN
BEARING CAP : 55.81 KN
BOLT CAP : 43.83 KN
NO. OF BOLTS REQD. : 3