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STRESS RESULT OF SOLID BEAM

Son Nguyen
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Hi all,

I am trying to interpret the solid result using an example as captured below. I model a simple beam with cross section of 1mx2m, the span is 10m. Theoretically, the max moment at mid point of the beam Mmax = 125kNm, the section modulus of the beam is W = bh^2/6 = 1*2^2/6 = 2/3 m3, then the max. stress at mid point of the beam is Mmax/W = 125/(2/3) = 187.5 kN/m2 = 0.1875 N/mm2. The problem is the Staad solid stress result is quite different with the above theoretical calculation. As captured in the second picture below, the stress distribution at the mid point of the beam is not symmetric from the topmost fiber to the bottom-most fiber. The max Sxx stress at the bottom fiber is about 0.073 N/mm2, whereas the minimum Sxx stress at the top fiber is about -0.143 N/mm2.

Could any one help me clarify why there are differences here or my comparison model was wrong somewhere?

Thanks,

My model:

----------------------------------------------------------------------

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 11-Oct-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0.5 0 0; 3 1 0 0; 4 1.5 0 0; 5 2 0 0; 6 2.5 0 0; 7 3 0 0;
8 3.5 0 0; 9 4 0 0; 10 4.5 0 0; 11 5 0 0; 12 5.5 0 0; 13 6 0 0;
14 6.5 0 0; 15 7 0 0; 16 7.5 0 0; 17 8 0 0; 18 8.5 0 0; 19 9 0 0;
20 9.5 0 0; 21 10 0 0; 22 0 0.5 0; 23 0.5 0.5 0; 24 1 0.5 0;
25 1.5 0.5 0; 26 2 0.5 0; 27 2.5 0.5 0; 28 3 0.5 0; 29 3.5 0.5 0;
30 4 0.5 0; 31 4.5 0.5 0; 32 5 0.5 0; 33 5.5 0.5 0; 34 6 0.5 0;
35 6.5 0.5 0; 36 7 0.5 0; 37 7.5 0.5 0; 38 8 0.5 0; 39 8.5 0.5 0;
40 9 0.5 0; 41 9.5 0.5 0; 42 10 0.5 0; 43 0 1 0; 44 0.5 1 0; 45 1 1 0;
46 1.5 1 0; 47 2 1 0; 48 2.5 1 0; 49 3 1 0; 50 3.5 1 0; 51 4 1 0;
52 4.5 1 0; 53 5 1 0; 54 5.5 1 0; 55 6 1 0; 56 6.5 1 0; 57 7 1 0;
58 7.5 1 0; 59 8 1 0; 60 8.5 1 0; 61 9 1 0; 62 9.5 1 0; 63 10 1 0;
64 0 1.5 0; 65 0.5 1.5 0; 66 1 1.5 0; 67 1.5 1.5 0; 68 2 1.5 0;
69 2.5 1.5 0; 70 3 1.5 0; 71 3.5 1.5 0; 72 4 1.5 0; 73 4.5 1.5 0;
74 5 1.5 0; 75 5.5 1.5 0; 76 6 1.5 0; 77 6.5 1.5 0; 78 7 1.5 0;
79 7.5 1.5 0; 80 8 1.5 0; 81 8.5 1.5 0; 82 9 1.5 0; 83 9.5 1.5 0;
84 10 1.5 0; 85 0 2 0; 86 0.5 2 0; 87 1 2 0; 88 1.5 2 0; 89 2 2 0;
90 2.5 2 0; 91 3 2 0; 92 3.5 2 0; 93 4 2 0; 94 4.5 2 0; 95 5 2 0;
96 5.5 2 0; 97 6 2 0; 98 6.5 2 0; 99 7 2 0; 100 7.5 2 0; 101 8 2 0;
102 8.5 2 0; 103 9 2 0; 104 9.5 2 0; 105 10 2 0; 106 0 0 0.5;
107 0.5 0 0.5; 108 1 0 0.5; 109 1.5 0 0.5; 110 2 0 0.5; 111 2.5 0 0.5;
112 3 0 0.5; 113 3.5 0 0.5; 114 4 0 0.5; 115 4.5 0 0.5; 116 5 0 0.5;
117 5.5 0 0.5; 118 6 0 0.5; 119 6.5 0 0.5; 120 7 0 0.5; 121 7.5 0 0.5;
122 8 0 0.5; 123 8.5 0 0.5; 124 9 0 0.5; 125 9.5 0 0.5; 126 10 0 0.5;
127 0 0.5 0.5; 128 0.5 0.5 0.5; 129 1 0.5 0.5; 130 1.5 0.5 0.5;
131 2 0.5 0.5; 132 2.5 0.5 0.5; 133 3 0.5 0.5; 134 3.5 0.5 0.5;
135 4 0.5 0.5; 136 4.5 0.5 0.5; 137 5 0.5 0.5; 138 5.5 0.5 0.5;
139 6 0.5 0.5; 140 6.5 0.5 0.5; 141 7 0.5 0.5; 142 7.5 0.5 0.5;
143 8 0.5 0.5; 144 8.5 0.5 0.5; 145 9 0.5 0.5; 146 9.5 0.5 0.5;
147 10 0.5 0.5; 148 0 1 0.5; 149 0.5 1 0.5; 150 1 1 0.5; 151 1.5 1 0.5;
152 2 1 0.5; 153 2.5 1 0.5; 154 3 1 0.5; 155 3.5 1 0.5; 156 4 1 0.5;
157 4.5 1 0.5; 158 5 1 0.5; 159 5.5 1 0.5; 160 6 1 0.5; 161 6.5 1 0.5;
162 7 1 0.5; 163 7.5 1 0.5; 164 8 1 0.5; 165 8.5 1 0.5; 166 9 1 0.5;
167 9.5 1 0.5; 168 10 1 0.5; 169 0 1.5 0.5; 170 0.5 1.5 0.5;
171 1 1.5 0.5; 172 1.5 1.5 0.5; 173 2 1.5 0.5; 174 2.5 1.5 0.5;
175 3 1.5 0.5; 176 3.5 1.5 0.5; 177 4 1.5 0.5; 178 4.5 1.5 0.5;
179 5 1.5 0.5; 180 5.5 1.5 0.5; 181 6 1.5 0.5; 182 6.5 1.5 0.5;
183 7 1.5 0.5; 184 7.5 1.5 0.5; 185 8 1.5 0.5; 186 8.5 1.5 0.5;
187 9 1.5 0.5; 188 9.5 1.5 0.5; 189 10 1.5 0.5; 190 0 2 0.5;
191 0.5 2 0.5; 192 1 2 0.5; 193 1.5 2 0.5; 194 2 2 0.5; 195 2.5 2 0.5;
196 3 2 0.5; 197 3.5 2 0.5; 198 4 2 0.5; 199 4.5 2 0.5; 200 5 2 0.5;
201 5.5 2 0.5; 202 6 2 0.5; 203 6.5 2 0.5; 204 7 2 0.5; 205 7.5 2 0.5;
206 8 2 0.5; 207 8.5 2 0.5; 208 9 2 0.5; 209 9.5 2 0.5; 210 10 2 0.5;
211 0 0 1; 212 0.5 0 1; 213 1 0 1; 214 1.5 0 1; 215 2 0 1; 216 2.5 0 1;
217 3 0 1; 218 3.5 0 1; 219 4 0 1; 220 4.5 0 1; 221 5 0 1; 222 5.5 0 1;
223 6 0 1; 224 6.5 0 1; 225 7 0 1; 226 7.5 0 1; 227 8 0 1; 228 8.5 0 1;
229 9 0 1; 230 9.5 0 1; 231 10 0 1; 232 0 0.5 1; 233 0.5 0.5 1;
234 1 0.5 1; 235 1.5 0.5 1; 236 2 0.5 1; 237 2.5 0.5 1; 238 3 0.5 1;
239 3.5 0.5 1; 240 4 0.5 1; 241 4.5 0.5 1; 242 5 0.5 1; 243 5.5 0.5 1;
244 6 0.5 1; 245 6.5 0.5 1; 246 7 0.5 1; 247 7.5 0.5 1; 248 8 0.5 1;
249 8.5 0.5 1; 250 9 0.5 1; 251 9.5 0.5 1; 252 10 0.5 1; 253 0 1 1;
254 0.5 1 1; 255 1 1 1; 256 1.5 1 1; 257 2 1 1; 258 2.5 1 1; 259 3 1 1;
260 3.5 1 1; 261 4 1 1; 262 4.5 1 1; 263 5 1 1; 264 5.5 1 1; 265 6 1 1;
266 6.5 1 1; 267 7 1 1; 268 7.5 1 1; 269 8 1 1; 270 8.5 1 1; 271 9 1 1;
272 9.5 1 1; 273 10 1 1; 274 0 1.5 1; 275 0.5 1.5 1; 276 1 1.5 1;
277 1.5 1.5 1; 278 2 1.5 1; 279 2.5 1.5 1; 280 3 1.5 1; 281 3.5 1.5 1;
282 4 1.5 1; 283 4.5 1.5 1; 284 5 1.5 1; 285 5.5 1.5 1; 286 6 1.5 1;
287 6.5 1.5 1; 288 7 1.5 1; 289 7.5 1.5 1; 290 8 1.5 1; 291 8.5 1.5 1;
292 9 1.5 1; 293 9.5 1.5 1; 294 10 1.5 1; 295 0 2 1; 296 0.5 2 1;
297 1 2 1; 298 1.5 2 1; 299 2 2 1; 300 2.5 2 1; 301 3 2 1; 302 3.5 2 1;
303 4 2 1; 304 4.5 2 1; 305 5 2 1; 306 5.5 2 1; 307 6 2 1; 308 6.5 2 1;
309 7 2 1; 310 7.5 2 1; 311 8 2 1; 312 8.5 2 1; 313 9 2 1; 314 9.5 2 1;
315 10 2 1; 316 10 0 5; 317 0 0 5; 318 5 0 5;
MEMBER INCIDENCES
161 317 318; 162 318 316;
ELEMENT INCIDENCES SOLID
1 106 107 128 127 1 2 23 22; 2 107 108 129 128 2 3 24 23;
3 108 109 130 129 3 4 25 24; 4 109 110 131 130 4 5 26 25;
5 110 111 132 131 5 6 27 26; 6 111 112 133 132 6 7 28 27;
7 112 113 134 133 7 8 29 28; 8 113 114 135 134 8 9 30 29;
9 114 115 136 135 9 10 31 30; 10 115 116 137 136 10 11 32 31;
11 116 117 138 137 11 12 33 32; 12 117 118 139 138 12 13 34 33;
13 118 119 140 139 13 14 35 34; 14 119 120 141 140 14 15 36 35;
15 120 121 142 141 15 16 37 36; 16 121 122 143 142 16 17 38 37;
17 122 123 144 143 17 18 39 38; 18 123 124 145 144 18 19 40 39;
19 124 125 146 145 19 20 41 40; 20 125 126 147 146 20 21 42 41;
21 127 128 149 148 22 23 44 43; 22 128 129 150 149 23 24 45 44;
23 129 130 151 150 24 25 46 45; 24 130 131 152 151 25 26 47 46;
25 131 132 153 152 26 27 48 47; 26 132 133 154 153 27 28 49 48;
27 133 134 155 154 28 29 50 49; 28 134 135 156 155 29 30 51 50;
29 135 136 157 156 30 31 52 51; 30 136 137 158 157 31 32 53 52;
31 137 138 159 158 32 33 54 53; 32 138 139 160 159 33 34 55 54;
33 139 140 161 160 34 35 56 55; 34 140 141 162 161 35 36 57 56;
35 141 142 163 162 36 37 58 57; 36 142 143 164 163 37 38 59 58;
37 143 144 165 164 38 39 60 59; 38 144 145 166 165 39 40 61 60;
39 145 146 167 166 40 41 62 61; 40 146 147 168 167 41 42 63 62;
41 148 149 170 169 43 44 65 64; 42 149 150 171 170 44 45 66 65;
43 150 151 172 171 45 46 67 66; 44 151 152 173 172 46 47 68 67;
45 152 153 174 173 47 48 69 68; 46 153 154 175 174 48 49 70 69;
47 154 155 176 175 49 50 71 70; 48 155 156 177 176 50 51 72 71;
49 156 157 178 177 51 52 73 72; 50 157 158 179 178 52 53 74 73;
51 158 159 180 179 53 54 75 74; 52 159 160 181 180 54 55 76 75;
53 160 161 182 181 55 56 77 76; 54 161 162 183 182 56 57 78 77;
55 162 163 184 183 57 58 79 78; 56 163 164 185 184 58 59 80 79;
57 164 165 186 185 59 60 81 80; 58 165 166 187 186 60 61 82 81;
59 166 167 188 187 61 62 83 82; 60 167 168 189 188 62 63 84 83;
61 169 170 191 190 64 65 86 85; 62 170 171 192 191 65 66 87 86;
63 171 172 193 192 66 67 88 87; 64 172 173 194 193 67 68 89 88;
65 173 174 195 194 68 69 90 89; 66 174 175 196 195 69 70 91 90;
67 175 176 197 196 70 71 92 91; 68 176 177 198 197 71 72 93 92;
69 177 178 199 198 72 73 94 93; 70 178 179 200 199 73 74 95 94;
71 179 180 201 200 74 75 96 95; 72 180 181 202 201 75 76 97 96;
73 181 182 203 202 76 77 98 97; 74 182 183 204 203 77 78 99 98;
75 183 184 205 204 78 79 100 99; 76 184 185 206 205 79 80 101 100;
77 185 186 207 206 80 81 102 101; 78 186 187 208 207 81 82 103 102;
79 187 188 209 208 82 83 104 103; 80 188 189 210 209 83 84 105 104;
81 211 212 233 232 106 107 128 127; 82 212 213 234 233 107 108 129 128;
83 213 214 235 234 108 109 130 129; 84 214 215 236 235 109 110 131 130;
85 215 216 237 236 110 111 132 131; 86 216 217 238 237 111 112 133 132;
87 217 218 239 238 112 113 134 133; 88 218 219 240 239 113 114 135 134;
89 219 220 241 240 114 115 136 135; 90 220 221 242 241 115 116 137 136;
91 221 222 243 242 116 117 138 137; 92 222 223 244 243 117 118 139 138;
93 223 224 245 244 118 119 140 139; 94 224 225 246 245 119 120 141 140;
95 225 226 247 246 120 121 142 141; 96 226 227 248 247 121 122 143 142;
97 227 228 249 248 122 123 144 143; 98 228 229 250 249 123 124 145 144;
99 229 230 251 250 124 125 146 145; 100 230 231 252 251 125 126 147 146;
101 232 233 254 253 127 128 149 148;
102 233 234 255 254 128 129 150 149;
103 234 235 256 255 129 130 151 150;
104 235 236 257 256 130 131 152 151;
105 236 237 258 257 131 132 153 152;
106 237 238 259 258 132 133 154 153;
107 238 239 260 259 133 134 155 154;
108 239 240 261 260 134 135 156 155;
109 240 241 262 261 135 136 157 156;
110 241 242 263 262 136 137 158 157;
111 242 243 264 263 137 138 159 158;
112 243 244 265 264 138 139 160 159;
113 244 245 266 265 139 140 161 160;
114 245 246 267 266 140 141 162 161;
115 246 247 268 267 141 142 163 162;
116 247 248 269 268 142 143 164 163;
117 248 249 270 269 143 144 165 164;
118 249 250 271 270 144 145 166 165;
119 250 251 272 271 145 146 167 166;
120 251 252 273 272 146 147 168 167;
121 253 254 275 274 148 149 170 169;
122 254 255 276 275 149 150 171 170;
123 255 256 277 276 150 151 172 171;
124 256 257 278 277 151 152 173 172;
125 257 258 279 278 152 153 174 173;
126 258 259 280 279 153 154 175 174;
127 259 260 281 280 154 155 176 175;
128 260 261 282 281 155 156 177 176;
129 261 262 283 282 156 157 178 177;
130 262 263 284 283 157 158 179 178;
131 263 264 285 284 158 159 180 179;
132 264 265 286 285 159 160 181 180;
133 265 266 287 286 160 161 182 181;
134 266 267 288 287 161 162 183 182;
135 267 268 289 288 162 163 184 183;
136 268 269 290 289 163 164 185 184;
137 269 270 291 290 164 165 186 185;
138 270 271 292 291 165 166 187 186;
139 271 272 293 292 166 167 188 187;
140 272 273 294 293 167 168 189 188;
141 274 275 296 295 169 170 191 190;
142 275 276 297 296 170 171 192 191;
143 276 277 298 297 171 172 193 192;
144 277 278 299 298 172 173 194 193;
145 278 279 300 299 173 174 195 194;
146 279 280 301 300 174 175 196 195;
147 280 281 302 301 175 176 197 196;
148 281 282 303 302 176 177 198 197;
149 282 283 304 303 177 178 199 198;
150 283 284 305 304 178 179 200 199;
151 284 285 306 305 179 180 201 200;
152 285 286 307 306 180 181 202 201;
153 286 287 308 307 181 182 203 202;
154 287 288 309 308 182 183 204 203;
155 288 289 310 309 183 184 205 204;
156 289 290 311 310 184 185 206 205;
157 290 291 312 311 185 186 207 206;
158 291 292 313 312 186 187 208 207;
159 292 293 314 313 187 188 209 208;
160 293 294 315 314 188 189 210 209;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17185e+007
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-005
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY
161 162 PRIS YD 2 ZD 1
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 21 106 126 211 231 316 317 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
ELEMENT LOAD SOLID
61 TO 80 141 TO 160 FACE 4 PRESSURE GY -10 -10 -10 -10
MEMBER LOAD
161 162 UNI GY -10
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
ELEMENT LOAD SOLID
20 40 60 80 100 120 140 160 FACE 5 PRESSURE GX 10 10 10 10
PERFORM ANALYSIS
FINISH

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