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Mechanical analyse on Chinese traditional wooden stuctures

Abstract:

This thesis was written by Mr Wang Tian, and translated by Hudong Li from Chinese into Korean. It is the first thesis to make a detailed analyse on Chinese traditional architectures. At nowadays engineers can solve very troublesome structural problems, because they have enough knowledge about mechanics and can be aided by computer. But how could those craftsmen perform such task thousands of years ago? Why the wooden structures can stand there for so long time? Did the builders grasped enough mechanics? Or they just succeeded occasionally? After read this thesis, you will find out that the Chinese builders of thousands of years ago did know how to construct the wooden buildings using perfect knowledge on materials, mechanics, and know how to make the advnatages of standarnized design to build buildings quickly and perfectly. Do not believe? Then read the following thesis.

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��ÅÀý[Ëáï¹]¶ó´Â ��ÍÀº ¾Æ¸¶µµ µÎ Á¾·ùÀÇ ¹®Á¦¸¦ ÇØ��áÇÏ��â À��ÇÑ Á¶Ä¡·Î º¸¿©Áø´Ù. ù ¹øÂ��´Â ºø¹ï¿½ï¿½ÀÌ ï¿½ï¿½â¿Íµé »çÀÌÀÇ ï¿½ï¿½áÇÕºÎ(Ì¿ùêÝ»)·Î ¹ÝÇâ(Úãú¾)µÇ¾î Ä��ÅõÇϴ ��ÍÀ» ¹æÁöÇϴ ��ÍÀÌ´Ù. ÁöºØ��â¿Í¸¦ ¹è¿­¹æ¹ýÀº ÀϹÝÀûÀ¸·Î "»óºÎ¿¡¼­ 4ºÐ(ÝÂ)À» ÁßøÇÏ¿©, ÇϺο¡¼­ 6ºÐÀ» ³²ï¿½ï¿½â´Â ��ÍÀÌ´Ù"; ����·¯¹Ç·Î ¸¸ÀÏ Á��¼ï¿½ï¿½ÁöºØÀ» Àû¿ëÇÑ´Ù¸é, ����¸² 3-3¿¡¼­ º¸À̴ ��Íó·³ ��â¿Í ¾Õ¿¡ Æ´ÀÌ ³ªÅ¸³¯ ��ÍÀÌ´Ù. ºñ·Ï ȸ(üé) µîÀ» ¹Ù¸ï¿½ï¿½À¸·Î½á ÀÌ Æ´À» ¸·À» ¼ö´Â ÀÖÁö¸¸, ��â¿Âº¯È­ ¶ï¿½ï¿½¹®¿¡ ºñ��¡ ³»¸ï¿½ï¿½ ¶ï¿½ï¿½¿¡´Â ºø¹ï¿½ï¿½ÀÌ ÀÌÆ´À» µû¶ó siphon Çö»óÀÌ ¹ß»ýÇÒ ¼ö ÀÖ´Ù. ÇÏÁö¸¸ ��ÅÀýÀÌ ÀÖ´Â ÁöºØÀº ��â¿ÍµéÀÌ ï¿½ï¿½î¼ï¿½ï¿½À» µû¶ó ¹è¿­µÇ¸ç, ����¸² 3-4¿¡¼­ º¸¿©ÁØ ÇüÅÂ¿Í ï¿½ï¿½ï¿½ÀÌ ï¿½ï¿½â¿Í µÚ¿¡ ÀÖ´Â Æ´ÀÌ Å¬¼ö·Ï, siphon Çö»óÀº ´õ ¹Ì¾àÇÏ¿©, ºø¹ï¿½ï¿½ÀÇ Ä��Åõ¸¦ ¹æÁöÇÒ ¼ö ÀÖ´Ù.









����¸² 3-3. ��â¿Í»çÀÌÀÇ Æ´(Üî) ����¸² 3-4. ��â¿Í»çÀÌÀÇ Æ´(Üî)

¾Õ¿¡ ÀÚ¸®Çϴ ��æ¿ì Åð¿¡ ÀÚ¸®Çϴ ��æ¿ì














����¸² 3-5. µÎ ��¡Áö ÁöºØÀÇ ºñ��³

µÎ ¹øÂ�� ¹®Á¦´Â ¾Æ¸¶µµ ��ÇÃà¹ï¿½ï¿½ÀÇ ¿¹¼úÀû Çü»ó��ú ��ü��è��¡ Àִ ��Íó·³ º¸ÀδÙ. ��í´ë��ÇÃà¹ï¿½ï¿½ÀÇ Ã³¸¶´Â µ¹Ãâ��Ÿ®µµ ��æ¾î¼­, ��âµÕ Áß½ÉÃà¿¡¼­ ºÎ¿¬[Þ«í­]³¡ï¿½ï¿½îÁö 280ºÐ(ÝÂ)¿¡ À̸¥´Ù. ¸¸ÀÏ 1µîÀçÀÇ ï¿½ï¿½Ç¹ï¿½ï¿½À̶ó¸é, 280ºÐÀº 5m Á��µµï¿½ï¿½¡ µÈ´Ù. ¸¸¾à¿¡ ÁöºØÀÌ Á��¼ï¿½ï¿½ÇüŶó¸é, ���� Çü»óÀº »»»»ÇÏ��í, ¿ìµÐÇÑ ¿Ü��ü(èâκ)À» ��®ï¿½ï¿½ÔµÈ´Ù. ��ÅÀýÁöºØÀº ¿¬ÇÏï¿½ï¿½í ºÎµå·´ï¿½ï¿½í, ¿ì¾ÆÇÑ ï¿½ï¿½î¼ï¿½ï¿½À» Çü¼ºÇÑ´Ù. ��ԴÙ��¡ ¿ë¸¶·ç, Ä¡¹Ì, ¼öµÎ µîÀ» ¼³Ä¡ÇÏ¿©, ¸Õ ���¿¡¼­ º¸¸é ÁöºØÀº ³¯¾Æ��¡´Â »õ¿Í ���Àº Çü»óÀ¸·Î º¸ÀδÙ. ÀÌ Á¡¿¡¼­ ��ÅÀý[Ëáï¹]Àº ��ÇÃ࿹¼úÀÇ ¿ä��¸ ¶ï¿½ï¿½¹®À̶óï¿½ï¿½í º¼ ¼ö ÀÖ´Ù.


ì£ Ã³¸¶ ¼­ï¿½ï¿½î·¡[��æË]¿Í µ¿¿¬[ô��æË]

¡¶¿µÁ¶¹ý½Ä¡·¿¡´Â "æË, îîå¥, îîó­ì»øÖæêñýå¥"(¡¶¿µÁ¶¹ý½Ä¡·Á¦2��Ç)¶ó´Â ��â¼ú(ÑÀâû)ÀÌ ÀÖ´Ù. ���� ¶æÀº ¼­ï¿½ï¿½î·¡ï¿½ï¿½¡ ÇÏÁßÀ» Àü´ÞÇÏ´Â ¿ªÇÒÀÌ Àִٴ ��ÍÀÌ´Ù. ����·¸´Ù¸é ¾î¶»ï¿½ï¿½Ô ÇÏÁßÀ» Àü´ÞÇÒ��î? Çϳª´Â ÁöºØÇÏÁßÀ» µµ¸®·Î ³»·Á ÀüÇÏ´Â ¹æ¹ýÀ̸ç, ´Ù¸¥ Çϳª´Â µ¿¿¬[ô��æË]À¸·ÎºÎÅÍ ¿©·¯ ¼­ï¿½ï¿½î·¡¸¦ ��ÅÃÄ Ã³¸¶ ¼­ï¿½ï¿½î·¡[��æË]��îÁö ÀüÇÏ´Â ¹æ½ÄÀÌ´Ù. ¹ï¿½ï¿½·Ð ÇÑÂÊ ¹æ½Ä È��Àº ÀÌ µÎ ¹æ½ÄÀÌ ÇÔ²², ��á��¹Àº ÁöºØÇÏÁßÀ» ÁöÁöÇϴ ��ÍÀÌ´Ù. ¼­ï¿½ï¿½î·¡ÀÇ ´Ù¸¥ ¿ªÇÒÀº ��ÇÃà¹ï¿½ï¿½ÀÇ µµ¸®¸¦ ¿¬ï¿½ï¿½áÇÏ¿©, ÁöºØÀÇ ÀÏü¼ºÀ» ��­ÇÏï¿½ï¿½Ô Çϴ ��ÍÀÌ´Ù. ¼­ï¿½ï¿½î·¡ï¿½ï¿½¡ ¾ç��¡[åÄÊ­]¸¦ ¿¬ï¿½ï¿½áÇÏ¿©, ÁöºØÀ» º¸ï¿½ï¿½­Çϸç ��¡ï¿½ï¿½¸ÀÇ ÀÏü¼ºÀ» ��­È­ÇÏ´Â ¿ªÇÒÀº Hose Æ®·¯½ºï¿½ï¿½¸Á¶ÀÇ »óÇö(ß¾ú��)��ú ���´Ù. ÀÌ·¯ÇÑ ¿ªÇÒ��ú ¸ñ��¸Á¶ Áß ¼­ï¿½ï¿½î·¡ÀÇ ¸ñÀç ¿ë·®(éÄÕá)À» »ìÆ캸¸é ¼­ï¿½ï¿½î·¡´Â ´ë¸ñÀÛ[ÓÞÙÊíÂ]üÁ¦ÁßÀÇ Áß¿äÇÑ ºÎÀçÀÓÀ» ¾Ë ¼ö ÀÖ´Ù.

¼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½æÀÌ´Â À��ġ¿¡ µû¶ó ¼­·Î ´Ù¸£ï¿½ï¿½í, ��¡Àå ��ä ��ÍÀº ó¸¶ ¼­ï¿½ï¿½î·¡[��æË]À̸ç, ºÎ´ãÇÏ´Â ÇÏÁßµµ ��¡Àå Å©´Ù. ¼­ï¿½ï¿½î·¡ÀÇ Á�¡�æÀÌ Å©¸é µ¹Ãâ��æÀ̵µ ��æ¾îÁø´Ù. ºÎ¿¬[Þ«í­]ÀÇ µ¹Ãâ��æÀ̴ ó¸¶¼­ï¿½ï¿½î·¡ÀÇ µ¹Ãâ��æÀÌÀÇ 6/10¿¡ À̸¥´Ù. 󸶼­ï¿½ï¿½î·¡¿Í ºÎ¿¬ÀÇ µ¹Ãâ��æÀ̴ ǥ 27¿¡¼­ º¸¿©ÁÖ��í ÀÖ´Ù.

ºÎ¿¬ÀÌ ¾²·¯Áú ��ÍÀ» ¹æÁöÇÏ��â À��Çؼ­, ºÎ¿¬ÀÌ ¿ÜÃâ¸ñ¿¡¼­ µ¹ÃâÇϴ ��æÀÌ´Â ¿ÜÃâ¸ñ µÚ¿¡ ³²ï¿½ï¿½ÜÁø ��æÀÌ º¸´Ù ¹Ýµå½Ã ª¾Æ¾ß ÇÑ´Ù. ¿ÜÃâ¸ñ µÚÀÇ ï¿½ï¿½æÀ̴ ��øÆ��[øèíÂ]Á¾·ù¿¡ µû¶ó ´Ù¸£´Ù. 4Æ��ÀÛ¿¡¼­ 8Æ��ÀÛ��îÁö ��¢ï¿½ï¿½¢ÀÇ ï¿½ï¿½æÀÌ´Â 30, 60, 90, 120, 150 ºÐ(ÝÂ)ÀÌ´Ù. 8Æ��ÀÛÀÇ ï¿½ï¿½æ¿ì¿¡ ºÎ¿¬Àº ÁÖ½É��îÁö ��¥ ÇÊ¿ä��¡ ¾ø´Ù. ÇÏÁö¸¸ ¾ÈÀüÀ» À��ÇÏ¿© ºÎ¿¬Àº ÁÖ½ÉÀ» Áö³ª¼­, ÇÏÁßµµ¸®[ù»øÁ��]À���îÁö ³õÀÌï¿½ï¿½Ô µÈ´Ù. (����¸² 3-6)













����¸² 3-6. ó¸¶ ¼­ï¿½ï¿½î·¡[��æË]ÀÇ µµÇØ

ºÎ¿¬Àº ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ ´ÜºÎ(Ӯݻ)¿¡ À��ġÇϸç, ���� À��ÀÇ ÇÏÁßÀº ó¸¶ ¼­ï¿½ï¿½î·¡¿Í ���Áö¸¸, ³ªï¿½ï¿½¡´Â ��æÀÌ��¡ ª��⠶��¹®¿¡ ���� ÀÀ·ÂÀ» ��è»êÇÒ ÇÊ¿ä��¡ ¾ø´Ù. ¶ï¿½ï¿½¹®¿¡ 󸶼­ï¿½ï¿½î·¡¸¦ ��è»êÇÒ ¶ï¿½ï¿½ ºÎ¿¬Àº 󸶼­ï¿½ï¿½î·¡ÀÇ ÀϺκÐÀ¸·Î ��è»êÇÏ¿©, 󸶼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½æÀÌ´Â ºÎ¿¬³¡¿¡¼­ ��è»êÇÑ´Ù.

¿¹¸¦ µé¾î ½Ê��¡¿¬¿Á[ä��ʭæËè©], ��øÆ��´Â 8Æ��ÀÛ[8øèíÂ], ����¸®ï¿½ï¿½í ó¸¶ ¼­ï¿½ï¿½î·¡ µ¹Ãâ��æÀÌ 80ºÐ[ÝÂ] ºÎ¿¬µ¹Ãâ��æÀÌ 48ÝÂ, ����¸®ï¿½ï¿½í 2µîÀç[ì£Ôõî��]ÀÇ ï¿½ï¿½Ç¹ï¿½ï¿½À̶ó¸é ´ÙÀ½ï¿½ï¿½ú ���ÀÌ ï¿½ï¿½è»êµÈ´Ù.(����¸² 3-7a)

��

¼­ï¿½ï¿½î·¡ÀÇ ÆòÀå[øÁíþ]: 48+80+150+150=428 ÝÂ

¼­ï¿½ï¿½î·¡ÀÇ »çÀå[ÞØíþ]: 428/COS

{ 25}^{¡£ }

��

=475 ÝÂ

ó¸¶ ¼­ï¿½ï¿½î·¡´Â ��¢ï¿½ï¿½¢ ¿ÜÃâ¸ñ[�֮�۳], Áֽɵµ¸®[ñºÔéÜî��], ����¸®ï¿½ï¿½í ÇÏÁßµµ¸®[ù»øÁ��]·Î ÁöÅʵÇ��í Àִµ¥, ����¸²3-7¿¡¼­ ¿ìô´Ü[éÚô����]´Â ÁöÁöÇÏ´Â ¿ªÇÒÀÌ ¾ø¾î¼­ »ý·«µÈ´Ù.

ÇÏÁß��è»ê:

ó¸¶ ¼­ï¿½ï¿½î·¡ ÀÚÁß: Á�¡�æÀº 9ºÐÀÌ��í, Ç¥11À» Âü��íÇÏ¿©, ÀÚÁßÀº 0.27 ÐÅ/Ý ÀÌ´Ù.

ÁöºØÇÏÁß: Ç¥6-2¸¦ Âü��íÇÏ¿©, ÁöºØÇÏÁßÀº

15.0 ÐÅ/ {100 ÝÂ}^{2 }

��

ÀÌ´Ù.

ó¸¶ ¼­ï¿½ï¿½î·¡¸¶´Ù ¹ÞÄ¡´Â ÁöºØÀÇ ÆøÀº 18ºÐÀÌ´Ù. µû¶ó¼­:

ó¸¶ ¼­ï¿½ï¿½î·¡ ÇÏÁß:

15.0 TIMES { 18} over {100 } =2.7 ÐÅ/ÝÂ

��

ÀÌ´Ù.

ÇÕ��è: 0.27+ 0.27= 2.97 ÐÅ/Ý ÀÌ´Ù.

ÁöºØÀÇ ¼öÁ��¹æÇâÀÇ ÇÏÁßÀº:

��

Q=2.97cos { 25}^{¡£} { 30}^{' }=2.7

��

ÐÅ/ÝÂ ÀÌ´Ù.

ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ ÈÚ ¸ð¸àÆ®¿Í ÁöÁ¡ ¹Ý·Â(ÚãÕô)ÀÇ ï¿½ï¿½è»ê:

��

{ M}_{ B} { l}_{ 2} +2 { M}_{ C}( { l}_{ 2}+ { l}_{ 3})=- { 2q { l}`_{2} ^{3 } } over {4 }

ÀÌ ¼ö½ÄÁß:

{ l}_{ 1} = { l}_{2 }=167, { l}_{1 } =143

��

{ M}_{ B}=- { 1} over {2} q { l}`_{ 1} ^{2 }

=- { 1} over {2} TIMES 2.7 TIMES { 143}^{ 2} =-27606.0

��

- { 2q { l}`_{2 } ^{3 } } over { 4} =- { 2 TIMES 2.7 TIMES { 167}^{ 3} } over { 4}=-6287575.0

����·¯¹Ç·Î:

��

-27606.0 TIMES 167+2 { M}_{c} (167+167)=-6287575.0

��

{ M}_{C}=-2511.0

ÐÅ TIMES ÝÂ

��

ÀÌ´Ù. (����¸² 3-7b)

ÁöÁ¡ÀÇ Àü´Ü·Â ��è»ê:

Àü´Ü·Â:

{ Q}`_{B } ^{' } =-386.1

��

ÐÅ

��

{ Q}`_{B } ^{'' } =225.5+ { { M}_{C } - { M}_{B } } over { { l}_{2 } } =375.8

��

ÐÅ

��

{ Q}`_{ C} ^{ ''}=225.5+ { { M}_{D } - { M}_{C } } over { { l}_{2 } } =245.5

��

ÐÅ

��

{ Q}`_{ C} ^{ '} =-225.5+150.3=-75.2

��

ÐÅ

��

{ Q}`_{ D} ^{' } =-225.5+15.0=-210.5

��

ÐÅ

¹Ý·Â ��è»ê:

¿ÜÃâ¸ñÀÇ ¹Ý·Â:

{ N}_{ B} = { Q}`_{B } ^{'' }- { Q}`_{B } ^{' }=375.8-(-286.1)=762.0

��

ÐÅ

Áֽɵµ¸®:

{ N}_{C }= { Q}`_{C } ^{'' }- { Q}`_{C } ^{' }=245.5-(-75.2)=320.7

��

ÐÅ

Áßµµ¸®:

{ N}_{D }=210.5

ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ ÀÀ·Â ��è»ê: ¿ÜÃâ¸ñ¿¡¼­ minusÈÚ¸ð¸àƮ��¡ ��¡Àå Å©´Ù:

��

{ M}_{B }=-27606.0ÐÅ TIMES ÝÂ

ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ Á�¡�æÀº 9ºÐÀÌ��í, Ç¥28À» Âü��íÇÏ¿©, ´Ü¸é��è¼öÀÎ Z=72

��

sigma = { 27606.0} over {72 }=383.0 ÐÅ/{ ÝÂ}^{2 } }<645 ÐÅ / { ÝÂ}^{2 }

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( Ç¥30À» Âü��íÇÏ¿©)



























����¸² 3-7. Àü´ç[îüÓÑ] ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½è»ê µµÇØ

ÀÌ ï¿½ï¿½á��ú¿¡ µû¶ó 󸶼­ï¿½ï¿½î·¡ÀÇ ÃÖ´ë(õÌÓÞ)ÀÀ·ÂÀº

383.0 ÐÅ/ { ÝÂ}^{2 }

��

³ª¹«Àç·áÀÇ ï¿½ï¿½­µµ(Ë­Óø) º¸´Ù ´õ ÀÛ��í, ºñ��³Àû ¾ÈÀüÇÏ´Ù. ÇÏÁö¸¸ ºÎÀç¿¡ ´ëÇÏ¿©, ÀÀ·Â »Ó¸¸ ¾Æ´Ï¶ó, ��­µµ(Ë��Óø)¸¦ ��è»êÇÒ ÇÊ¿äµµ ÀÖ´Ù. ÈÚ ¸ð¸àÆ®¸¦ ¹Þ´Â ÁÖ¿ä ºÎÀç´Â ¹Ýµå½Ã ��­µµ(Ë��Óø)·Î Á¦¾ÐµÇ¾î¾ß ÇÑ´Ù. ¿Ö³ÄÇϸé, ¸ñÀçÀÇ Åº¼ºï¿½ï¿½è¼ö´Â ÀÛÀº ��ÍÀÌ��í, ���� ũ��â´Â ¿ø¸ñ(ê«ÙÊ)Ä¡¼ö·Î Á¦ÇѵǾî ÀÖ��⠶��¹®ÀÌ´Ù. ��­µµ(Ë��Óø)Á¶ï¿½ï¿½ÇÀ» ¸¸Á·ÇÏ´Â ºÎÀ縸 »ç¿ëÇÒ ¼ö¹Û¿¡ ¾ø´Ù.

ºÎ¿¬Àº ó¸¶ ¼­ï¿½ï¿½î·¡ ³¡Á¡¿¡ ÀÚ¸®ÇÏ¿©, ó¸¶ ¼­ï¿½ï¿½î·¡¿Í ���ÀÌ º¯Çü(Ü��û¡)ÇÏ��⠶��¹®¿¡, 󸶼­ï¿½ï¿½î·¡ÀÇ Ã³ÁüÀ» ��¸ÇÒ ¶ï¿½ï¿½ 󸶼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½æÀÌ´Â ºÎ¿¬ ³¡Á¡¿¡¼­ ��è»êÇÑ´Ù. Àç·á¿ªÇÐÀÇ ï¿½ï¿½ø½Ä¿¡ µû¶ó¼­:

��

f= { qa} over { 24EJ}( { b}^{3 } -6 { a}^{2 } b-3 { a}^{ 3} )

ÀÌ ï¿½ï¿½ø½Ä¿¡¼­ q=2.7, a= 143, b=167

Ç¥31µû¶ó

E=4.96 TIMES { 10}^{ 5}

��

, Ç¥28µû¶ó

J=322

����·¯¹Ç·Î:

��

f= { 2.7 TIMES 143} over {24 TIMES 4.96 TIMES { 10}^{ 5} TIMES 322 }( { 167}^{ 3}-6 TIMES { 167}^{ 2 } TIMES 143-3 TIMES { 143}^{ 2} )

��

=-2.46ÝÂ=4.3cm


»ó´ë(ßÓÓß)óÁü:

f/l= { 2.46} over {143 }= { 1} over {58 }> { 1} over {150 }


1/150Àº Çö´ë ¸ñ��¸Á¶ÀÇ Ç¥ÁØ��ԹüÀÌ´Ù. ºÎÀç��­µµ(Ë��Óø)¿¡ ´ëÇÑ ¿ä��¸´Â ¿¾³¯ï¿½ï¿½ú ¿À´Ã³¯ÀÇ Â��ÀÌ��¡ Å©Áö ¾Ê´Ù. ¾Õ¿¡¼­ ¾òÀº ��è»ê��á��ú¸¦ º¸¸é ºÎ¿¬ ³¡Á¡¿¡¼­ 2.46ºÐ(4.3cm )ÀÇ Ã³ÁüÀÌ ¹ß»ýÇÑ´Ù. ÀÌ ï¿½ï¿½á��ú´Â ºÐ¸íÈ�� Å« ��ÍÀÌ´Ù. ÀÌ´Â 9ºÐÀÇ Ã³¸¶¼­ï¿½ï¿½î·¡ Á�¡�æÀÌ ¾à��£ ÀÛÀº ��ÍÀ̸ç ��­µµ(Ë��Óø)��¡ ºÎÁ·ÇÑ ï¿½ï¿½ÍÀ» ÀǹÌÇÑ´Ù. ����·¸Áö¸¸ ½ÇÁ¦ Á¸ÀçÇÏ��í Àִ ��ÇÃà¹ï¿½ï¿½¿¡¼­ ÀÌ·¸ï¿½ï¿½Ô Å« óÁüÀº ³ªÅ¸³ªÁö ¾Ê¾Ò´Ù. ¿¹¸¦ µé¸é ºÒ��ûç(ÝÖÏàÞÑ)¸ñž(ÙÊ��²), ¼ï¿½ï¿½È­»ç(à¼ü��ÞÑ)ÀÇ ´ë¿õÀü, À¶Èï»ç(ëØýéÞÑ)ÀÇ ¸¶´ÏÀü(Ø��Òùîü)µî ��ǹ��ÀÇ Ã³¸¶¼­ï¿½ï¿½î·¡ Á�¡�æÀº ¸ðµÎ 9ÝÂÀÌ��í, õ³â(ô¶Ò´)ÀÌ»ó¿¡ ï¿½ï¿½ÉÃļ­ 󸶼­ï¿½ï¿½î·¡ï¿½ï¿½¡ ¸¹ÀÌ ÃÄÁø ÀûÀÌ ¾ø¾ú´Ù. µû¶ó¼­ 9ÝÂÀÇ Á�¡�æÀº ÀÛÀº ��ÍÀ̶ó ÇÒ ¼ö ¾ø´Ù. ¡¶¿µÁ¶¹ý½Ä¡·ÀÇ ï¿½ï¿½ÔÁ��Àº ¸ðµÎ "¿©·¯ ½Ã´ëÀÇ ï¿½ï¿½øÀå(ÍïíÝ)µéÀÌ »ó¼¼ÇÏï¿½ï¿½Ô ¿¬ï¿½ï¿½¸ÇÏ¿© ¾òÀº ��á��ú"ÀÌ´Ù. ����·¯¹Ç·Î ¾ÕÀÇ ï¿½ï¿½è»êÀº Ÿ´çÇÏÁö ¾ÊÀº Á¡ÀÌ ÀÖÀ» ��ÍÀÌ´Ù.

¡¶¿µÁ¶¹ý½Ä¡·Á¦ 5 ��ÇÁß <æË>¿¡ ��üÇÑ ÁÖ¼®À» º¸¸é "¸ðµç ¼­ï¿½ï¿½î·¡¸¦ ¼³Ä¡ÇÒ ¶ï¿½ï¿½ ¼­ï¿½ï¿½î·¡ ¸Ó¸®[æËÔé]´Â ¹ØÀ¸·Î, ¼­ï¿½ï¿½î·¡ ²¿¸®[æËÚ­]´Â À��·Î ¼³Ä¡ÇؾßÇÑ´Ù"¶óï¿½ï¿½í µÇ¾î ÀÖ´Ù. ���� ¶æÀº ¼­ï¿½ï¿½î·¡µéÀ» ¹èÄ¡ÇÒ ¶ï¿½ï¿½ ¹Ýµå½Ã ��½Àº ´Ü(Ó®)À» ¹Ø¿¡ ³õ��í, ��¡´Â ´ÜÀ» À��¿¡ ³õ¾Æ¾ß ÇÑ´Ù´Â ¸»ÀÌ´Ù. ����·¸Áö¸¸ ¡¶¿µÁ¶¹ý½Ä¡·¿¡¼­ 󸶼­ï¿½ï¿½î·¡Á�¡�æÀÎ 9ÝÂÀÌ ï¿½ï¿½½Àº ºÎºÐÀÎÁö, ��¡´Â ºÎºÐÀÎÁö, È��Àº Áß��£ºÎºÐÀÎÁö ¾î´À ºÎºÐÀÇ Á�¡�æÀ̶ó´Â ��ÍÀ» ¼³¸íÇÏÁö´Â ¾Ê¾Ò´Ù. Çö´ë ¸ñ��¸Á¶¿¡ ´ëÇÑ ï¿½ï¿½ÔÁ��¿¡ µû¸£¸é ºÎÀçÀÇ Á�¡�æÀº ¸ðµÎ ��¡´Â ºÎºÐÀÇ Á�¡�æÀÌ´Ù. ��¡´Â ºÎºÐ¿¡¼­ ��½Àº ºÎºÐ��îÁö ¸Å 1m¸¶´Ù 1cm¸¦ Áõ��¡½ÃŲ´Ù. ¸¸ÀÏ 9ÝÂÀ̶ó´Â ��ÍÀÌ ï¿½ï¿½¡´Â ºÎºÐÀÇ Á�¡�æ¶ó¸é, ��æÀÌ��¡ 167ÝÂÀÇ Ã³¸¶¼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½¡¿îµ¥ Á�¡�æÀº 9.84ÝÂÀÌ��í, ��½Àº ºÎºÐÀÇ Á�¡�æÀº 10.7 ÝÂÀÌ´Ù. ¸¸ÀÏ 9ÝÂÀÌ ï¿½ï¿½½Àº ºÎºÐÀÇ Á�¡�æÀ» À̶ó¸é, ��¡¿îµ¥ Á�¡�æÀº 8.71ÝÂÀÌ��í, ��¡´Â ºÎºÐÀÇ Á�¡�æÀº 8.71ÝÂÀÌ´Ù. ÀüÁ¦ÀûÀ¸·Î ºÐ¼®Çϸé, 9ÝÂÀÇ Á�¡�æÀ» ��¡¿îµ¥ ºÎºÐÀÇ Á�¡�æÀ¸·Î º¸´Â ��ÍÀÌ ´õ Àû´çÇÏ´Ù. ÀÌ·¸ï¿½ï¿½Ô Çϸé 󸶼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½¡´Â ºÎºÐÀÇ Á�¡�æÀÌ 8.17 ÝÂÀÌ��í, ��ÅÀÇ ¿µÇâÀÌ ¾ø´Ù.

´ÙÀ½Àº ó¸¶ ¼­ï¿½ï¿½î·¡ ��¡¿îµ¥ÀÇ Á�¡�æÀ» 9ºÐÀ¸·Î ´Ù½Ã 󸶼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½­µµ(Ë��Óø)¸¦ ��è»êÇÑ ï¿½ï¿½ÍÀÌ´Ù. 󸶼­ï¿½ï¿½î·¡ ��¡¿îµ¥ Á�¡�æÀÌ 9ÝÂÀ̶ó¸é, ¿ÜÃâ¸ñ[�֮�۳]¿¡¼­ 󸶼­ï¿½ï¿½î·¡ÀÇ Á�¡�æÀº 11.5ºÐÀÌ´Ù. 11.5ºÐÀÇ Á�¡�æÀ¸·Î ºÎ¿¬ÀÇ Ã³ÁüÀ» ��¸Çϸé, ���� ��á��ú´Â 0.9ÝÂ(1.6cm)ÀÌ´Ù. ����·¯¹Ç·Î:

»ó´ë óÁü:

f/l= { 0.9} over {143 } = { 1} over { 158} APPROX { 1} over {150 }


ÀÌ ï¿½ï¿½á��ú´Â Çö´ë ¸ñ��¸Á¶ÀÇ Ã³Áü Ç¥ÁØ¿¡ Àß ¸Â´Â´Ù. 0.9ÝÂÀÇ Ã³ÁüÀº ÁöºØÀÇ ï¿½ï¿½â´É��ú Çü»ó¿¡ ´ëÇÑ ¿µÇâÀÌ ï¿½ï¿½ÅÀÇ ¾ø´Ù. À̸¦ º¸¸é ¡¶¿µÁ¶¹ý½Ä¡·¿¡¼­ 󸶼­ï¿½ï¿½î·¡ Á�¡�æÀ» 9ºÐÀ¸·Î ��ÔÁ��ÇÑ ï¿½ï¿½ÍÀÌ Å¸´çÇÑ ï¿½ï¿½ÍÀÌ´Ù.

³ª¾Æ��¡ µ¿¿¬[ô��æË]ÀÇ ÇÏÁßÀº 󸶼­ï¿½ï¿½î·¡¸¦ Á¦¿ÜÇÑ ´Ù¸¥ ¼­ï¿½ï¿½î·¡º¸´Ù ¾à��£ ´õ ũ��⠶��¹®¿¡ ����ÀÇ ÀÀ·ÂÀ» ��¸ÇØ¾ß ÇÑ´Ù.

¾Õ¿¡¼­ ¾ð��ÞÇÑ ï¿½ï¿½ÅÀý[Ëáï¹]��ø½ÄÀ» Àû¿ëÇÏ¿©, Á¾µµ¸®ÀÇ ³ôÀÌÀÎ

{ h}_{0 }

��

¸¦ ��¸ÇÑ´Ù.

��

{ h}_{ 0}= { 458(600-0.000745 { x}^{2 } )} over {458+x }

��

��

BECAUSE x=0 THEREFORE { h}_{ 0} =600ÝÂ

»óÁßµµ¸®[ß¾øÁ��]ÀÇ ³ôÀÌ´Â:

��


{ h}_{ 1} = { 458(600-0.000745 TIMES { 150}^{2 } )} over {458+150 } =440ÝÂ

µ¿¿¬[ô��æË]ÀÇ ï¿½ï¿½æÀ̸¦ ��¸Çϸé:

��

l= SQRT { { 150}^{ 2} + { (600-440)}^{2 } }=220ÝÂ

µ¿¿¬ÀÇ ï¿½ï¿½æ»çµµ(ÌËÞØÓø)

cos alpha = { 150} over {220 }=0.68



��

THEREFORE alpha = { 47}^{¡£} { 6}^{' }

µ¿¿¬¿¡¼­ ³»¸®´Â ¼öÁ��ÇÏÁßÀº :

2.97cos { 47}^{¡£ } { 6}^{' } =2.0

��

ÐÅ/ÝÂ ÀÌ´Ù.

µ¿¿¬ ��¡¿îµ¥ÀÇ ÈÚ¸ð¸àÆ®´Â:

��

M= { 1} over { 8} TIMES 2.0 TIMES { 220}^{2 } =12100 ÐÅ TIMES ÝÂ

µ¿¿¬ ÀÀ·ÂÀ» ��¸Çϸé:

Z=71.57

��

alpha = { 12100} over {71.57 } =168ÐÅ/ { ÝÂ}^{2 }<645 ÐÅ/ { ÝÂ}^{2 }

��

(¾ÈÀü)

µ¿¿¬ ��¡¿îµ¥ÀÇ Ã³ÁüÀ» ��¸Çϸé:

��

f= { 5} over {384 } { q { l}^{4 } } over { EJ} = { 5} over {384 } { 2.0 TIMES { 220}^{4 } } over { 4.96 TIMES { 10}^{ 5} TIMES 322} =0.37ÝÂ

��

ÀÌ´Ù.

»ó´ë(ßÓÓß) óÁüÀº:

��

f/l=0.37/220= { 1} over {595 }< { 1} over {150 }

��

ÀÌ´Ù.

ÀÌ ï¿½ï¿½á��ú¸¦ ºÐ¼®Çϸé, µ¿¿¬ÀÇ ¾ÈÀü��è¼ö��¡ ³Ê¹« Å©Áö¸¸(3.8 ¹è), 󸶼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½ÍÀº Àû´çÇÑ ï¿½ï¿½ÍÀÌ´Ù. 󸶼­ï¿½ï¿½î·¡ ÀÌ¿Ü¿¡ ��⟠¼­ï¿½ï¿½î·¡ÀÇ Á�¡�æÀÌ ¿Ö Å©ï¿½ï¿½Ô µÇ´Â��¡¿¡ ��üÇÑ ÀÌÀ¯¿¡ ´ëÇØ ï¿½ï¿½íÀº ¿¬ï¿½ï¿½¸ï¿½ï¿½¡ ��â´ëµÈ´Ù.

¾Õ¿¡¼­´Â Àü´ç[îüÓÑ]¿¡ 󸶼­ï¿½ï¿½î·¡ÀÇ ¼ö·Â[áôÕô]»óŸ¦ ºÐ¼®ÇÏ¿´´Ù. ÀÌ ï¿½ï¿½âȸ¿¡ 󸶼­ï¿½ï¿½î·¡¿¡ ¿ÜÃâ¸ñ[�֮�۳]��ú ÇÏÁßµµ¸®[ù»øÁ��]¿¡ ³»¸®´Â ¾Ð·ÂÀ» ��¸ÇÏ¿©, ´ÙÀ½¿¡ ¿©·¯ ÀåÀÇ ï¿½ï¿½è»êÀ» À��Çؼ­ ÇÏÁßÁ¶ï¿½ï¿½ÇÀ» ÁÖ��â·Î ÇÏ��í, û´ç[ôæÓÑ] 󸶼­ï¿½ï¿½î·¡¸¦ ��è»êÇÏ��íÀÚ ÇÑ´Ù.

¿¹¸¦ µé¾î 6Æ��ÀÛ, 3µµ(ß²Ô¯), 󸶼­ï¿½ï¿½î·¡ µ¹Ãâ��æÀÌ 75ÝÂ, ºÎ¿¬ ��æÀÌ 45ÝÂ, 3µîÀç, ��£ï¿½ï¿½ï¿½ï¿½[ÊàÎÆ]300ÝÂ, 󸶼­ï¿½ï¿½î·¡Á�¡�æ 8ÝÂ, µµ¸® Á�¡�æ18ÝÂ, 󸶼­ï¿½ï¿½î·¡ï¿½ï¿½£ ��Ÿ® 17ÝÂÀ̶ó¸é,

ÁöºØÇÏÁß ï¿½ï¿½¸ÇÏ��â.

ÁöºØÇÏÁßÀº Ç¥ 4-2¿¡ µû¶ó

11.1 ÐÅ/ { 100ÝÂ}^{2 }

��

ÀÌ´Ù. 󸶼­ï¿½ï¿½î·¡ ��æÀÌ¿¡ µû¶ó ¸Å ºÐ[ÝÂ]ÀÇ ÇÏÁßÀº

��

11.1 TIMES 17/100=1.9 ÐÅ/ÝÂ

��

ÀÌ´Ù.

󸶼­ï¿½ï¿½î·¡ ÀÚÁßÀº Ç¥11¿¡ µû¶ó 0.16 ÐÅ/Ý ÀÌ´Ù.

ÇÕ��è:

1.9+0.16=2.06 ÐÅ

󸶼­ï¿½ï¿½î·¡ï¿½ï¿½¡ ¹Þ´Â ¼öÁ��ÇÏÁßÀº:

��

2.06 cos { 21}^{¡£ }=1.923 ÐÅ/ÝÂ APPROX 2.0 ÐÅ/ÝÂ


��è»êµµ¸éÀº ����¸²3-8a¿Í ���´Ù:

{ l}_{1 }=129, { l}_{2 }=98, { l}_{3 } =161,

��

{ M}_{D }=0

��

{ M}_{B }=- { 1} over {2 } q { l}`_{1} ^{2 } =- { 1} over {2 } TIMES 2.0 TIMES { 129}^{ 2} =-16641

ÐÅ TIMES ÝÂ

C ÁöÁ¡ÀÇ ? ¸ð¸àÆ®¸¦ ��¸Çϸé:

��

{ M}_{B } { l}_{2 }+2 { M}_{C }( { l}_{ 2}+ { l}_{3 })=- { q { l}`_{2 } ^{3 } } over {4 }- { q { l}`_{3 } ^{3 } } over {4 }

��

-16641 TIMES 98+2 { M}_{C } (98+161)=- { 2.0 TIMES { 98}^{ 3} } over {4 } - { 2.0 TIMES { 161}^{3 } } over {4 }

��

-1630818+518 { M}_{C }=-470596-2086640

��

{ M}_{C }=-1788

ÐÅ TIMES ÝÂ

��

(����¸² 3-8b)

ÁöÁ¡ÀÇ Àü´Ü·ÂÀº ����¸² 3-8c¿Í ���´Ù.

��

{ Q}`_{B } ^{' }=-258ÐÅ

��

{ Q}`_{B } ^{'' }=98+ { { M}_{C }- { M}_{B } } over { { l}_{2 } } =98+ { -1788+16641} over { 98}=250ÐÅ

��

{ Q}`_{C } ^{' }=-98+ { -1788+16641} over {98 }=54 ÐÅ

��

{ Q}`_{C } ^{'' }=161+ { { M}_{D }- { M}_{C } } over { { l}_{3 } }=161+ { 0+1788} over {161 }=172 ÐÅ

��

{ Q}_{D }=-161+ { 0+1788} over {161 }=-150 ÐÅ

ÁöÁ¡¿¡ ¹Ý·Â(ÚãÕô) ��¸ÇÏ��â:

��

{ N}_{B }= { Q}`_{B } ^{'' }- { Q}`_{B } ^{' }=250-(-258)=508 ÐÅ

��

( ¿ÜÃâ¸ñ[�֮�۳]¿¡¼­)

��

{ N}_{C }= { Q}`_{C } ^{'' }- { Q}`_{C } ^{' }=172-54=118 ÐÅ

��

(Áֽɵµ¸®[ñºÔéÜî��]¿¡¼­)

��

{ N}_{D }=0-(-150)=150 ÐÅ

��

(ÇÏÁßµµ¸®[ù»øÁ��]¿¡¼­)

��øÆ��´Â 7, 8 Æ��ÀÛ[øèíÂ]ÀÏ ¶ï¿½ï¿½ ��âµÕ Áß½ÉÃà¿¡¼­ 2µµ[Ô¯]ÀÇ ï¿½ï¿½Å¸®¿¡ ¼³Ä¡ÇÏ´Â µµ¸®´Â ¿ìô´Ü[éÚô����]À̶ó��í ÇÑ´Ù. ¾Õ¿¡¼­ Àü´ç[îüÓÑ] ó¸¶ ¼­ï¿½ï¿½î·¡À» ºÐ¼®ÇÒ ¶ï¿½ï¿½´Â À̸¦ »ý·«ÇÏ¿´´Ù. ��á��¹ ÀÌ ºÎÀç´Â ¾î¶² ÁöºØÇÏÁßÀ» ÁöÅÊÇÏ´Â ¿ªÇÒÀ» ÇÒ��î? ��è»êµµ¸éÀº ����¸² 3-9a¿Í ���´Ù.

󸶼­ï¿½ï¿½î·¡ ÆòÀå[øÁíþ]:

128+90+60+150=428ÝÂ

󸶼­ï¿½ï¿½î·¡ »çÀå[ÞØíþ]:

428/cos { 25}^{¡£ } { 30}^{' } =476ÝÂ

󸶼­ï¿½ï¿½î·¡´Â ¿ÜÃâ¸ñ(BÁöÁ¡), ¿ìô´Ü([éÚô����], CÁöÁ¡), Áֽɵµ¸®([ñºÔàÜî��], DÁöÁ¡), ÇÏÁßµµ¸®(EÁöÁ¡)À¸·Î ÁöÁöµÇ��í ÀÖ´Ù.

ÇÏÁß ï¿½ï¿½¸ÇÏ��â:

ó¸¶ ¼­ï¿½ï¿½î·¡ ÀÚÁß: 2µîÀç, Á�¡�æ 9ºÐ, ¼­·Î��£ÀÇ ï¿½ï¿½Å¸® 18ºÐ, Ç¥11¿¡ µû¶ó ¸Å ºÐÀÇ ÀÚÁßÀº 0.27 ÐÅ/Ý ÀÌ´Ù.

ÁöºØÇÏÁß: 2.72 ÐÅ/Ý (¾Õ¿¡¼­ Àü´ç[îüÓÑ]ÀÇ ï¿½ï¿½æ¿ì¸¦ Âü��íÇÏ¿©)

ÁöºØ ÀûÀçÇÏÁß: Ç¥ 24¸¦ Âü��íÇÏ¿© 0.18ÐÅ/Ý ÀÌ´Ù.(¾Õ¿¡¼­ Àü´çÀ» ºÐ¼®ÇÒ ¶ï¿½ï¿½ ÁöºØ ÀûÀçÇÏÁßÀÌ ³Ê¹« ÀÛ��⠶��¹®¿¡ »ý·«µÇ¾ú´Ù.)

ÇÕ��è:

0.27=2.72+0.18=3.17 ÐÅ/ÝÂ

󸶼­ï¿½ï¿½î·¡ï¿½ï¿½¡ ¹ÞÀº ¼öÁ��ÇÏÁßÀº

3.17cos { 25}^{¡£ } { 30}^{' }=2.85ÐÅ/ÝÂ

��

ÀÌ´Ù.

ÁöÁ¡ ÈÚ ¸ð¸àÆ®¿Í ¹Ý·Â ��¸ÇÏ��â: ����¸² 3-9b, 3-9c¿Í ���´Ù.

��

{ l}_{1 }=142, { l}_{2 }=100, { l}_{ 3}=67, { l}_{4 }=167

��

{ M}_{E }=0

��

{ M}_{ B}=- { 1} over {2 }q { l}`_{1 } ^{2 }=- { 1} over {2 } TIMES 2.85 TIMES { 142}^{2 }=-28734

ÐÅ TIMES ÝÂ

��

{ M}_{B } { l}_{2 }+2 { M}_{C }( { l}_{2 }+ { l}_{3 })+ { M}_{D } { l}_{2 }=- { q { l}`_{2 } ^{3 } } over {4 }- { q { l}`_{2 } ^{3 } } over {4 }

��

-28734 TIMES 100+2 { M}_{C }(100+67)+ { M}_{D} TIMES 100=- { 2.85 TIMES { 100}^{3 } } over {4 }- { 2.85 TIMES { 67}^{3 } } over {4 }

��

334 { M}_{C }+100 { M}_{D }=1946606

��

---��ç

��

{ M}_{C } { l}_{ 3}+2 { M}_{D }( { l}_{3 }+ { l}_{4 })+ { M}_{E } { l}_{3 }=- { q { l}`_{3 } ^{3 } } over {4 }- { q { l}`_{4 } ^{3 } } over {4 }

��

67 { M}_{C }+2 { M}_{D }(67+167)+0=- { 2.85 TIMES { 67}^{3 } } over {4 }- { 2.85 TIMES { 167}^{3 } } over {4 }

��

67 { M}_{ C} +468 { M}_{D }=-3532736

��

��

{ M}_{D }= { -3532736-67 { M}_{C } } over {468 }

��

---��è

��è¿Í ��çÀ» ��áÇÕÇϸé,

��

334 { M}_{C }+100 TIMES { -3532736-67 { M}_{C } } over {468 } =1946606

��

{ M}_{C }=8450

��

ÐÅ TIMES ÝÂ

��

{ M}_{C }

��

��ú ��ç·Î ³õÀ¸¸é,

��

100 { M}_{D }+334 TIMES 8450=1946606

��

{ M}_{D }=-8757

��

ÐÅ TIMES ÝÂ


Àü´Ü·Â ��¸ÇÏ��â:

��

{ Q}`_{B } ^{' }=-405 ÐÅ

��

{ Q}`_{B } ^{'' }=143+ { { M}_{C }- { M}_{B } } over { { l}_{2 } }=143+ { 8450-8757} over { 100} =315 ÐÅ

��

{ Q}`_{C } ^{' }=-143+ { { M}_{C }- { M}_{B } } over { { l}_{2 } }=29 ÐÅ

��

{ Q}`_{C} ^{'' }=95+ { { M}_{D }- { M}_{C } } over { { l}_{3 } }=95+ { -8757-8450} over { 67}=-162 ÐÅ

��

{ Q}`_{D } ^{' } =-95+ { -8575-8450} over {67 }=-352 ÐÅ

��

{ Q}`_{ D} ^{'' }=238+ { { M}_{E }+ { M}_{D } } over { { l}_{4 } }=238+ { 0+8575} over {167 }=290 ÐÅ

��

{ Q}`_{E } ^{' }=-238+ { 0+8575} over {167 } =-186 ÐÅ

































����¸² 3-8. û´ç[ôæÓÑ] ó¸¶ ¼­ï¿½ï¿½î·¡ÀÇ ï¿½ï¿½è»ê µµÇØ

¹Ý·Â ��¸ÇÏ��â:

��

{ N}_{B } = { Q}`_{B } ^{'' }- { Q}`_{B } ^{' }=315+405=720 ÐÅ

��

¿ÜÃâ¸ñ(BÁöÁ¡)¿¡¼­

��

{ N}_{C }= { Q}`_{C } ^{'' }- { Q}`_{C } ^{' }=-162-29=-191 ÐÅ

��

¿ìô´Ü([éÚô����], CÁöÁ¡)¿¡¼­

��

{ N}_{D }= { Q}`_{D } ^{'' }- { Q}^{' }=290+350=642 ÐÅ

��

Áֽɵµ¸®([ñºÔàÜî��], DÁöÁ¡)¿¡¼­

��

{ N}_{E }=186 ÐÅ

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Ãâ¸ñµµ¸® Áß¾Ó ÃÖ´ë(õÌÓÞ)ÀÇ Ã³ÁüÀ» ��¸ÇÏ��â:

(

a=31, { }_{ } , l=188, { }^{ } J=22500

��

)

��

f= { q { l}^{2 } } over {16EJ }( { 5 { l}^{2 } } over {24 }- { a}^{2 })= { 42.3 TIMES { 188}^{2 } } over {16 TIMES 4.96 TIMES { 10}^{5 } TIMES 22500 }( { 5 TIMES { 188}^{2 } } over {24 }- { 31}^{2 })

��

��

=0.05359 ÝÂ

��

ÀÌ´Ù.

â¹æ[�Yäþ]ÀÇ ï¿½ï¿½¡¿îµ¥ ÃÖ´ë(õÌÓÞ)óÁüÀ» ��¸ÇÏ��â:(Ç¥ 18-2 ¿¡ µû¶ó

P=1990 ÐÅ

��

ÀÌ´Ù. ��è»ê ½ºÆÇÀÎ

l=220 ÝÂ

��

(����¸² 6-3), ´Ü¸é ¸éÀûÀÌ

30 TIMES 20 { ÝÂ}^{2 }

��

ÀÌ´Ù.)

��

��

f= { P { l}^{3 } } over {48EJ }= { 1990 TIMES { 220}^{3 } } over {48 TIMES 4.96 TIMES { 10}^{5 } TIMES 45000 } =0.01977 ÝÂ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀÌ

q=29 ÐÅ/ÝÂ

��

ÀÌ´Ù, ��è»ê½ºÆÇÀÌ 210 ÝÂÀ¸·Î Á��ÇÏ��í, Á�¡�æÀÌ 21Ý ÀÌ´Ù. (����¸² 6-4). µû¶ó¼­ ��¡¿îµ¥ÀÇ Ã³ÁüÀÌ:

��

f= { 5q { l}^{4 } } over {384 TIMES 4.96 TIMES { 10}^{ 5} TIMES 9547 } =0.155 ÝÂ

��

ÀÌ´Ù.








����¸² 6-4. ÇÏÁßµµ¸®ÀÇ ï¿½ï¿½è»ê µµÇØ ï¿½ï¿½ï¿½ï¿½¸² 6-5. ��è»ê µµÇØ

ÀÌ·¯ÇÑ ï¿½ï¿½á��ú¸¦ ºÐ¼®ÇÑ´Ù¸é, ÇÏÁßµµ¸®ÀÇ Ã³ÁüÀº Á¦ÀÏ Å©ï¿½ï¿½í, ´ÙÀ½¿¡´Â Ãâ¸ñµµ¸®ÀÇ Ã³ÁüÀÌ��í, â¹æÀÇ Ã³ÁüÀÌ ï¿½ï¿½¡Àå ÀÛÀº ��ÍÀ» ¾Ë ¼ö ÀÖ´Ù. µû¶ó¼­ ������͵éÀÌ ï¿½ï¿½ï¿½ÀÌ ÇÏÁßÀ» ÁöÁöÇÒ ¶ï¿½ï¿½ ÇÏÁßµµ¸®¿Í Ãâ¸ñµµ¸®´Â ¸ðµÎ â¹æ¿¡ ÇÏÁßÀ» ÀüÇØ ÁØ´Ù. ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀº ¾Ó(äé)À» ÅëÇÏ¿© Ãâ¸ñµµ¸®ÀÇ ÇÏÁß��ú »ó¼âÇÑ ÈÄ¿¡ ³ª¸ÓÁöÀÇ ºÎºÐÀº â¹æÀ¸·Î ÀüÇÑ´Ù. ����·¡¼­ Ãâ¸ñµµ¸®´Â ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀ» ��ÕÇüÇÏ´Â ¿ªÇÒÀ» ÇÏ��í ÀÖ´Ù. ¿ø·¡ ¾Ó(äé)À» ¼³Ä¡ÇÏ´Â ¸ñÀûÀº ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀ¸·Î Ãâ¸ñµµ¸®¸¦ ÆòÇüÇϴ ��ÍÀÌÁö¸¸, ½ÇÁ¦ÀûÀÎ »óȲÀº ¹Ý´ë·Î µÇ¾ú´Ù. ��ԴÙ��¡ Ãâ¸ñµµ¸®ï¿½ï¿½¡ ��âµÕ Áß½ÉÃà¿¡ ��¡ï¿½ï¿½îÀÌ ¿Ã¼ö·Ï ´õ Å« ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀ» »ó¼âÇÒ ¼ö ÀÖ´Ù.

ÀÌ ¼¼ ��¡ÁöÀÇ ºÎÀç´Â ��ä¹ÐÇÏï¿½ï¿½Ô ¿¬ï¿½ï¿½áµÈ´Ù¸é óÁüÀÌ ï¿½ï¿½ï¿½ï¿½Ô µÈ´Ù. µû¶ó¼­ ��¢ï¿½ï¿½¢ÀÇ ÇÏÁßÀ» ��¸ÇÒ ¼öÀÖ´Ù. ¿¹·Î¼­:

(ìé). À̵îÀç(ì£Ôõî��), ��£ï¿½ï¿½ï¿½ï¿½(ÊàÎÆ) 250ÝÂ, 1��³ÀÇ ï¿½ï¿½ø��£Æ��ÀÇ ï¿½ï¿½Ç¹ï¿½ï¿½ï¿½ú ���Àº ��æ¿ì¿¡¼­(����¸² 6-5):

ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀÇ ÀϺκÐÀº Áßµµ¸®[ñéøÁ��] ÇÏÁßÀÇ 1/2ÀÎ 17ÐÅ/Ý ÀÌ��í, ÀϺκÐÀº ¼­ï¿½ï¿½î·¡ÀÇ ÇÏÁßÀÎ

210/18=12 ÐÅ/ÝÂ

��

ÀÌ´Ù. µû¶ó¼­ ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀº ÇÕ��è 29 ÐÅ/ÝÂÀÌ��í

{ q}_{1 }¿Í { q}_{2 }

��

·Î ³ª´©¾î Á³´Ù.(����¸² 6-6) ÇÏÁßµµ¸®¿¡¼­ â¹æÀ¸·Î ÀüÇÏ´Â ÇÏÁßÀÎ

{ P}^{'' } =105 { q}_{2 }

��

ÀÌ��í(����¸² 6-2), Ãâ¸ñµµ¸®ï¿½ï¿½¡ â¹æ¿¡ ÀüÇÏ´Â ÇÏÁßÀº ¿ª½Ã

{ P}^{'' } =105 { q}_{2 }

��

ÀÌ´Ù.








����¸² 6-6. ÇÏ Áßµµ¸®ÀÇ ï¿½ï¿½è»ê µµÇØ

â¹æÀÇ ÇÏÁßÀ» ÇÕ��èÇÑ´Ù¸é:

P=2 { P}^{'' }+1990

��

ÐÅÀÌ´Ù.(��ø��£Æ��ÀÇ ÀÚÁß(í»ñì)ÀÌ 1990 ÐÅÀÌ´Ù.)

ÇÏÁßµµ¸® ��¡¿îµ¥ÀÇ Ã³ÁüÀº

{ q}_{1 }¿Í { q}_{2 }

��

¶ï¿½ï¿½¹®¿¡ »ý��ä óÁüÀÎ

{ f}_{1 }¿Í { f}_{ 2}

��

ÀÇ ÇÕ��èÀÌ´Ù.

��

J=9547

��

{ f}_{ 1}= { 5 { q}_{1 } { l}^{4 } } over {384EJ } = { 5 TIMES { 210}^{ 4 { q}_{1 } } } over {384 TIMES 4.96 TIMES { 10}^{ 5} TIMES 9547 } =0.00535 { q}_{ 1}

��

{ f}_{ 2}= { 3 { q}_{2 } { l}^{4 } } over {640EJ }= { 3 TIMES { 210}^{4 } { q}_{ 2} } over {640 TIMES 4.96 TIMES { 10}^{5 } TIMES 9547 } =0.001925 { q}_{2 }

â¹æÀº ´Ü¼øº¸·Î »ý��¢ÇÑ´Ù¸é, ��è»ê ½ºÆÇÀº

l=220 ÝÂ, { }_{ } J=45000

��

ÀÌ´Ù.

��

f= { P { l}^{3 } } over {48EJ }= { { 220}^{3 }P } over {48 TIMES 4.96 TIMES { 10}^{5 } TIMES 4500 } =0.0000099P

µû¶ó¼­:(

f= { f}_{1 }+ { f}_{2 }

��

)

��

0.00000P=0.00535 { q}_{1 }+0.001925 { q}_{2 }

��

BECAUSE { P}^{'' } =105 { q}_{2 }

��

THEREFORE P=2 { P}^{'' }+1990=210 { q}_{2 } +1990

��

BECAUSE { q}_{ 1}=q- { q}_{2 }

��

THEREFORE { q}_{ 1}=29- { q}_{2 }

����·¡¼­

{ q}_{2 }=24.59

��

ÀÌ´Ù. ÇÏÁßµµ¸®¿¡¼­ â¹æ¿¡ ÀüÇÏ´Â ÇÏÁßÀº:

��

{ P}^{'' } =105 { q}_{ 2} =105 TIMES 24.59=2582ÐÅ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®ÀÇ ½ÇÁ¦ÀûÀÎ ÇÏÁßÀº:

��

29 TIMES 250-2582=4668 ÐÅ

��

ÀÌ´Ù.

Ãâ¸ñµµ¸®ÀÇ ½ÇÁ¦ÀûÀÎ ÇÏÁßÀº:

��

{ 762} over {18 } TIMES 250 -2582=8000 ÐÅ

��

ÀÌ´Ù.

â¹æÀÇ ÇÏÁßÀº:

��

P=2 { P}^{'' }+1990=2582 TIMES 2 +1990=7554ÐÅ

��

ÀÌ´Ù.

â¹æÀº 7554ÐÅÀÇ ÇÏÁßÀ» ¹ÞÀ¸¸é º¸¿Í ���Àº ¿ªÇÒÀ» ÇÏ��í ÀÖ´Ù.

���� ÀÀ·ÂÀ» ��¸Çϸé:

��

M= { 1} over {4 } TIMES 7554 TIMES 220=415470 ÐÅ TIMES ÝÂ

��

sigma = { 415470} over {3000 }=138.5 ÐÅ / { ÝÂ}^{2 }

��

(Ç¥ 28¿¡ µû¶ó Z=3000)ÀÌ´Ù.

(ì£). ��£ï¿½ï¿½ï¿½ï¿½[ÊàÎÆ]375ÝÂÀÇ ï¿½ï¿½Ç¹ï¿½ï¿½¿¡¼­ â¹æ, ÇÏÁßµµ¸®[ù»øÁ��], Ãâ¸ñµµ¸®[�֮�۳]ÀÇ ÇÏÁß:

â¹æ ��¡¿îµ¥ ��ø��£Æ��ÀÌ 2��³ ÀÖ��í, ½ºÆÇ 345ÝÂ, ÇÏÁßµµ¸® Á�¡�æÀÌ 21Ý ÀÌ´Ù. ´ÜµÎü¸ñÁöÁ¡[Ó��ÔàôðÙÊò��ñ��]ÀÇ ½ºÆÇÀÌ 335ÝÂ, ÇÏÁß

q=29 ÐÅ/ÝÂ

��

ÀÌ´Ù.(����¸² 6-7):







����¸² 6-7. ÇÏÁßµµ¸®ÀÇ ï¿½ï¿½è»ê µµÇØ

ÇÏÁßµµ¸®ÀÇ Ã³ÁüÀ» ��¸ÇÏ��â:

��

{ f}_{ 1}= { 5 TIMES { 335}^{4 } { q}_{1 } } over {384 TIMES 4.96 TIMES { 10}^{5 } TIMES 9547 } =0.03463 { q}_{1 }

��

a=105, { }_{ } , alpha =105/335

��

, µû¶ó¼­:

��

{ f}_{2 }= { { q}_{2 } { a}^{2 } { l}^{2 } } over {240EJ }(5-2 { a}^{2 })= { { 105}^{2 } TIMES { 335}^{2 } { q}_{2 } } over {240 TIMES 4.96 TIMES { 10}^{5 } TIMES 9547 }(5-2 TIMES { 105} over {335 })

��

=0.00523 { q}_{2 }


â¹æÀÇ ÇÏÁßÀº ����¸³ 6-8��ú ���´Ù. â¹æ ��¡¿îµ¥ óÁü ��¸ÇÏ��â:

(

a=110, { }_{ } l=345, { }_{ } J=45000

��

)

��

f= { Pa { l}^{ 2} } over {24EJ }(3-4 { { a}^{2 } } over { { l}^{2 } })= { 110 TIMES { 345}^{2 } TIMES P } over {24 TIMES 4.96 TIMES { 10}^{5 } TIMES 45000 }(3-4 TIMES { { 110}^{2 } } over { { 345}^{2 } }=0.000063P

��

{ P}^{'' }= { 125+105} over {2 } { q}_{ 2}= { q}_{2 }= { 230} over {2 } { q}_{2 }

â¹æÀÇ ÇÏÁßÀ» ��¸ÇÏ��â:

��

P= 2{ P}^{'' } +1990=230 { q}_{2 }+1990

��

ÀÌ´Ù.

��

BECAUSE

f= { f}_{1 }+ { f}_{ 2}

��

{ q}_{1 } =q- { q}_{2 }

��

THEREFORE

0.000063P=0.03463 { q}_{1 }+0.00523 { q}_{2 }

��

0.000063(230 { q}_{2 }+1990)=0.0346(q- { q}_{2 })+0.00523 { q}_{2 }

��

{ q}_{2 }=20 ÐÅ/ÝÂ

��

ÀÌ´Ù.







����¸² 6-8. â¹æÀÇ ï¿½ï¿½è»ê µµÇØ

ÇÏÁßµµ¸®[ù»øÁ��]��¡ ºÐ´ãÇÏ´Â ÇÏÁßÀº:

��

29 TIMES 375-20(125+105)=6275 ÐÅ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®¿¡¼­ â¹æÀ¸·Î Àü´ÞÇÏ´Â ÇÏÁßÀº:

��

20(125+105)=4600ÐÅ

��

ÀÌ´Ù. (

{ P}^{'' }

��

)

ÇÏÁßµµ¸®ÀÇ ´Ü¸éÀÀ·ÂÀº 179 ÐÅ/Ý ÀÌ´Ù.

â¹æÀÇ ÇÏÁßÀº:

��

4600 TIMES 2+1990 TIMES 2=13180 ÐÅ

��

ÀÌ´Ù.

â¹æ ��¡¿îµ¥ ÀÀ·ÂÀ» ��¸ÇÏ��â:

��

M=110(4600+1990)=724900 ÐÅ TIMES ÝÂ

Ç¥29 ¿¡ µû¶ó Z=3000 ÀÌ´Ù.

��

sigma = { 724900} over {3000 } =242 ÐÅ/ { ÝÂ}^{2 }

Ãâ¸ñµµ¸®ÀÇ ÇÏÁßÀº 4600 ÐÅÀ» �㡧¼ÒÇÏï¿½ï¿½Ô µÈ´Ù. ����·¡¼­ ½ÇÁ¦ÀûÀÎ ÇÏÁßÀº:

��

42.3 TIMES 375-4600=11263ÐÅ

��

ÀÌ´Ù.

µû¶ó¼­ Ãâ¸ñµµ¸® ´Ü¸éÀÇ ÀÀ·ÂÀº

184 ÐÅ/ { ÝÂ}^{2 }


(ß²). û´ç[ôæÓÑ]¿¡¼­ â¹æÀÇ ÇÏÁß:

3µîÀç(ß²Ôõî��), ��£ï¿½ï¿½ï¿½ï¿½(ÊàÎÆ) 300ÝÂ, ��ø��£Æ�� 1 ��³, 6Æ��ÀÛ[6øèíÂ]ÀÇ ï¿½ï¿½øÆ��ÀÇ ôæÓÑ��ú ���Àº ��æ¿ì¿¡¼­ ¼­ï¿½ï¿½î·¡¸¶´Ù ÇÏÁßµµ¸®À¸·Î ÀüÇÏ´Â ÇÏÁßÀº 150 ÐÅÀÌ��í, µîºÐÆ��ÇÏÁßÀº

150/17=8.8 ÐÅ/ÝÂ

��

ÀÌ´Ù. û´ç[ôæÓÑ] ÁßÆò´ÜÀÇ ÇÏÁßÀº 7071 ÐÅÀ̸ç, ���� 1/2 Àº 3535 ÐÅÀÌ´Ù(Áï, 3535ÐÅÀÇ ÇÏÁßÀ» ÇÏÁßµµ¸®¿¡ ÀüÇØ ÁØ´Ù).

µû¶ó¼­ ÇÏÁßµµ¸®¿¡ ¹ÞÀº µîºÐÆ��ÇÏÁßÀ» ÇÕ��èÇÑ´Ù¸é:

��

q=8.8+ { 3535} over {300 } =20.4 ÐÅ/ÝÂ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®ÀÇ Á�¡�æÀº 18 ÝÂÀÌ��í, ½ºÆÇÀº 260 ÝÂÀÌ´Ù.

â¹æ, ÇÏÁßµµ¸®, Ãâ¸ñµµ¸®ÀÇ ÇÏÁß��ü��è´Â ����¸² 6-9¿Í ���´Ù.








����¸² 6-9. À��Æ��ÀÛ(ë»øèíÂ) ��øÆ��ÀÇ µµÇØ

��ø��£Æ��¸¶´Ù ÀÚÁßÀº 1605 ÐÅÀÌ´Ù.

â¹æÀÇ ÇÏÁßÀº:

��

P= { P}^{' }+ { P}^{'' }+1605

��

ÀÌ´Ù.

��

BECAUSE 90 { P}^{' }=150 { P}^{'' }

��

THEREFORE { P}^{' }= { 5} over {3 } { P}^{'' }

��

{ P}^{'' }=(q- { q}_{ 1}) { 260} over {2 }=130 { q}_{2 }

��

{ q}_{1 }=q- { q}_{2 }

ÇÏÁßµµ¸®ÀÇ ÇÏÁßÀº ����¸² 6-10��ú ���´Ù.






����¸² 6-10. ÇÏ Áßµµ¸®ÀÇ ï¿½ï¿½è»ê µµÇØ

��

{ q}_{1 }

��

ÀÎ ÇÏÁßÀº ÇÏÁßµµ¸® ��¡¿îµ¥¿¡ ÀÏÀ¸Å² óÁüÀ» ��¸ÇÏ��â:

(Ç¥ 31¿¡ µû¶ó

J=5153, { }_{ } , E=4.1 TIMES { 10}^{5 }

��

).

��

f= { 5 { q}_{1 } { l}^{4 } } over {384EJ } = { 5 TIMES { 260}^{4 } { q}_{1 } } over {384 TIMES 4.1 TIMES { 10}^{5 } TIMES 5153 } =0.0282 { q}_{1 }

��

��

{ q}_{2 }

��

ÀÎ ÇÏÁßÀº ÇÏÁßµµ¸® ��¡¿îµ¥¿¡ ÀÏÀ¸Å² óÁüÀ» ��¸ÇÏ��â:

��

f= { 3 { q}_{2 } { l}^{4 } } over {640EJ }= { 3 TIMES { 260}^{ 4} { q}_{2 } } over {640 TIMES 4.1 TIMES { 10}^{5 } TIMES 5153 } =0.01014 { q}_{2 }

��

â¹æÀÇ Ã³ÁüÀ» ��¸ÇÏ��â(

l=270, J=45000

��

):

��

f= { P { l}^{3 } } over {48EJ }= { { 270}^{3 }P } over {48 TIMES 4.1 TIMES { 10}^{5 } TIMES 45000 } =0.0000222P

��

��

BECAUSE

P= { P}^{' }+ { P}^{'' }+1605

��

(ºÎÀçµéÀÇ Ã³Áü��ú ����⠶��¹®¿¡)

��

THEREFORE

P= { 5} over {3 } TIMES 130 { q}_{2 }+130 { q}_{2 }+1605=346.67 { q}_{2 }+1605

��

µû¶ó¼­:

��

0.0000222P=0.0282 { q}_{1 }+0.01014 { q}_{2 }

��

0.0000222(346.67 { q}_{ 2}+1605)=0.0282(q- { q}_{2 })+0.01014 { q}_{2 }

��

0.02756 { q}_{2 }=0.53967

��

����·¡¼­:

��

{ q}_{2 }=19.6 ÐÅ /ÝÂ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®¿¡¼­ â¹æ¿¡ ÀüÇÏ´Â ÇÏÁßÀÎ

{ P}^{'' }

��

À» ��¸ÇÏ��â:

��

{ P}^{'' }=130 { q}_{2 }=130 TIMES 19.6=2548 ÐÅ

Ãâ¸ñµµ¸®¿¡¼­ â¹æ¿¡ ÀüÇÏ´Â ÇÏÁßÀÎ

{ P}^{' }

��

˼:

��

{ P}^{' }= { 5} over {3 } { P}^{'' }= { 5} over {3 } TIMES 2548=4247ÐÅ

{ l}_{0 }=375-62=313ÝÂ

��

ÀÌ´Ù.

����·¡¼­ â¹æÀÇ ÇÏÁßÀº:

��

P= { P}^{' }+ { P}^{'' }+1605=2548+4247+1605=8400 ÐÅ

��

ÀÌ´Ù.

ÇÏÁßµµ¸®ÀÇ ½ÇÁ¦ÀûÀÎ ÇÏÁßÀº:

��

20.4 TIMES 300-2548=3572ÐÅ

��

ÀÌ´Ù.

Ãâ¸ñµµ¸®ÀÇ ½ÇÁ¦ÀûÀÎ ÇÏÁßÀº:

��

30.35 TIMES 300-4247=4858 ÐÅ

��

ÀÌ´Ù.

(Á¦ 2Àå¿¡¼­ º¸¿©ÁØ ï¿½ï¿½Í��ú ���À¸¸ç ¼­ï¿½ï¿½î·¡ÀÇ ÇÏÁßÀº 516 ÐÅ À̸ç, 516/17=30.35 ÐÅ/ÝÂ)

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To be continued

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