케이블 길이와 장력 계산

양창현교수님의 구조역학 책에 있는 5-4 등분포하중을 받는 케이블 -포물선 과 3차 연립방정식으로 2차 포물선식을 계산하여 케이블 길이를 상호 비교 해보았다.
 
L=195m
h=4.041m

 
포물선의 길이 산정
포물선의 길이 산정은 아래 3가지 방법으로 검증하였다.
ⓐ3차연립방정식을 이용한 2차함수 공식

ⓑ등분포를 받는 케이블 공식(포물선)

ⓒ적분함수를 이용한 길이 산정

ⓐ3차연립방정식을 이용한 2차함수 공식
ⓑ등분포를 받는 케이블 공식(포물선)
ⓒ적분함수를 이용한 길이 산정
 
S= 195.22308172 구조역학 케이블 공식
S= 195.22308222 ⓐ좌표를 이용한 길이 산정
S= 195.22308222 ⓑ좌표를 이용한 길이 산정
S= 195.22308240 ⓒ적분함수를 이용한 길이 산정
 
길이 차이는 거의 없다.
 
 

 
 
 

 

케이블의 길이 및 장력계산.xlsx

0.31MB

엑셀 파일 받는 방법

1. 엑셀파일은 위 링크를 클릭하여 다운 받으시면 됩니다.
 

 
 
스크립트로 pline 그리기

SCRIPT를 이용하여 point, pline, text 입력하기

 
 
엑셀에서 3차 연립방정식 계산

엑셀에서 행렬을 3차연립방정식의 풀이

 
 
스크립트로 pline 그리기

pline
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173.5,118.847
173.6,118.854
173.7,118.86
173.8,118.867
173.9,118.873
174,118.88
174.1,118.886
174.2,118.893
174.3,118.899
174.4,118.906
174.5,118.912
174.6,118.919
174.7,118.925
174.8,118.932
174.9,118.939
175,118.945
175.1,118.952
175.2,118.958
175.3,118.965
175.4,118.972
175.5,118.978
175.6,118.985
175.7,118.992
175.8,118.998
175.9,119.005
176,119.012
176.1,119.018
176.2,119.025
176.3,119.032
176.4,119.038
176.5,119.045
176.6,119.052
176.7,119.058
176.8,119.065
176.9,119.072
177,119.079
177.1,119.085
177.2,119.092
177.3,119.099
177.4,119.106
177.5,119.113
177.6,119.119
177.7,119.126
177.8,119.133
177.9,119.14
178,119.147
178.1,119.154
178.2,119.16
178.3,119.167
178.4,119.174
178.5,119.181
178.6,119.188
178.7,119.195
178.8,119.202
178.9,119.209
179,119.216
179.1,119.222
179.2,119.229
179.3,119.236
179.4,119.243
179.5,119.25
179.6,119.257
179.7,119.264
179.8,119.271
179.9,119.278
180,119.285
180.1,119.292
180.2,119.299
180.3,119.306
180.4,119.313
180.5,119.32
180.6,119.327
180.7,119.335
180.8,119.342
180.9,119.349
181,119.356
181.1,119.363
181.2,119.37
181.3,119.377
181.4,119.384
181.5,119.391
181.6,119.399
181.7,119.406
181.8,119.413
181.9,119.42
182,119.427
182.1,119.434
182.2,119.442
182.3,119.449
182.4,119.456
182.5,119.463
182.6,119.47
182.7,119.478
182.8,119.485
182.9,119.492
183,119.5
183.1,119.507
183.2,119.514
183.3,119.521
183.4,119.529
183.5,119.536
183.6,119.543
183.7,119.551
183.8,119.558
183.9,119.565
184,119.573
184.1,119.58
184.2,119.587
184.3,119.595
184.4,119.602
184.5,119.609
184.6,119.617
184.7,119.624
184.8,119.632
184.9,119.639
185,119.647
185.1,119.654
185.2,119.661
185.3,119.669
185.4,119.676
185.5,119.684
185.6,119.691
185.7,119.699
185.8,119.706
185.9,119.714
186,119.721
186.1,119.729
186.2,119.736
186.3,119.744
186.4,119.752
186.5,119.759
186.6,119.767
186.7,119.774
186.8,119.782
186.9,119.789
187,119.797
187.1,119.805
187.2,119.812
187.3,119.82
187.4,119.828
187.5,119.835
187.6,119.843
187.7,119.851
187.8,119.858
187.9,119.866
188,119.874
188.1,119.881
188.2,119.889
188.3,119.897
188.4,119.904
188.5,119.912
188.6,119.92
188.7,119.928
188.8,119.935
188.9,119.943
189,119.951
189.1,119.959
189.2,119.967
189.3,119.974
189.4,119.982
189.5,119.99
189.6,119.998
189.7,120.006
189.8,120.013
189.9,120.021
190,120.029
190.1,120.037
190.2,120.045
190.3,120.053
190.4,120.061
190.5,120.069
190.6,120.077
190.7,120.084
190.8,120.092
190.9,120.1
191,120.108
191.1,120.116
191.2,120.124
191.3,120.132
191.4,120.14
191.5,120.148
191.6,120.156
191.7,120.164
191.8,120.172
191.9,120.18
192,120.188
192.1,120.196
192.2,120.204
192.3,120.212
192.4,120.22
192.5,120.228
192.6,120.237
192.7,120.245
192.8,120.253
192.9,120.261
193,120.269
193.1,120.277
193.2,120.285
193.3,120.293
193.4,120.301
193.5,120.31
193.6,120.318
193.7,120.326
193.8,120.334
193.9,120.342
194,120.351
194.1,120.359
194.2,120.367
194.3,120.375
194.4,120.383
194.5,120.392
194.6,120.4
194.7,120.408
194.8,120.416
194.9,120.425
195,120.433