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On shear stress

 

°íÃþ°Ç¹°Àº ÈÚ»Ó¸¸ ¾Æ´Ï¶ó Àü´Üµµ ÁöÁöÇÒ ¼ö ÀÖ´Â ½Ã½ºÅÛÀ» °¡Á®¾ß¸¸ ÇÑ´Ù.
[1] °Ç¹°Àº Ç㸮ºÎÀ§°¡ ¶Ò ²÷¾îÁü¿¡ ÀÇÇؼ­ Æı«µÇÁö ¾Ê¾Æ¾ß ÇÑ´Ù.
[2] Àü´Ü¿¡ ÀÇÇØ ³Ê¹« ¸¹ÀÌ º¯ÇüµÇ¾îµµ ¾ÈµÈ´Ù.

Tall buildings must have a system to resist shear as well as bending.
[1] The building must not break by shearing off.
[2] And the building must not strain too much from shear.

//ȨÁö±â ñÉ//¼ö½ÄÀÌ Á¦°øµÇÁö ¾Ê¾Æ¼­ ¼ö½ÄÀ» ´ÙÀ½°ú °°ÀÌ Ç¥ÇöÇÏ°Ú½À´Ï´Ù.
* : °öÇϱ⠱âÈ£, ** : Á¦°ö ±âÈ£, / : ³ª´©±â ±âÈ£, SQR : Á¦°ö±Ù ±âÈ£

//comment//Algebraic symbols are not provided by my NAMO editor, so they are expressed as follows instead.
* : multiplication, ** : square, / : division, SQR : square root

Àü´Üº¯Çüµµ¸¦ ÁöÁöÇÏ´Â À¯È¿¼ºÀº Àü´Ü°­¼ºÁö¼ö(shear rigidity index, SRI)¿¡ ÀÇÇؼ­ ÃøÁ¤µÈ´Ù. ¾î¶² ½Ã½ºÅÛ¿¡ ´ëÇؼ­µµ, ¸¸¾à Àü´Ü·ÂÀÌ S, ³ôÀÌ°¡ H, Ⱦº¯À§°¡ d, Àç·áÀÇ ºÎÇÇ°¡ V, ź¼º°è¼ö°¡ EÀ̸é Àü´Ü°­¼ºÁö¼ö´Â ´ÙÀ½°ú °°ÀÌ Á¤Àǵȴ٠:

Àü´Ü°­¼ºÁö¼ö = 250*(S*H**2)/(EVd)

·Î Á¤ÀǵȴÙ. ¿ÏÀüÇÑ ÆÇÀ̳ª º®ÀÇ °æ¿ì, Àü´Ü°­¼ºÁö¼ö´Â 100ÀÌ´Ù.

The effectiveness to resist shearing strain is measured by its Shear Rigidity Index, or SRI. For any system, if Shear is S, Height is H, Deflection is d(Delta with subscript s : original symbol in the article), Volume of Material is V, and Modulus of Elasticity is E, the Shear Rigidity Index is defined as :

SRI = 250*(S*H**2)/(EVd)

For a pure plate or wall, the SRI is set at 100.

¿À¸¥ÂÊÀÇ ±×¸²¿¡¼­ :

A. ÀÌ»óÀûÀÎ ½Ã½ºÅÛÀº °³±¸ºÎ°¡ ¾ø´Â ¿ÏÀüÇÑ ÆÇÀ̳ª º®ÀÌ´Ù.

In the drawings at the right :

A. The ideal system is a plate or wall without openings.

B. ´ÙÀ½ µÎ ¹ø°·Î ÀÌ»óÀûÀÎ Àü´Ü½Ã½ºÅÛÀº 45µµ·Î °æ»çÁø ´ë°¢¼± ¿þºêÀçÀÇ ³×Æ®¿öÅ©ÀÌ´Ù.:¼öÁ÷ºÎÀ糪 ±âµÕÀº ÈÚ ½Ã½ºÅÛ¿¡ ¼ÓÇϹǷΠÀü´Ü½Ã½ºÅÛÀÇ Àç·áºÎÇÇ°è»ê¿¡ Æ÷ÇÔµÇÁö ¾Ê´Â´Ù.) ÀÌ·± ½Ã½ºÅÛÀÇ °æ¿ì, Àü´Ü°­¼ºÁö¼ö´Â (5/8)*100=62.5ÀÌ´Ù. ÀÌ·± ½Ã½ºÅÛÀº ´ÙÀ½ ´ÞÀÇ ±Û¿¡ ¼Ò°³µÉ Erewhon Half-Mile Center¿¡¼­ »ç¿ëµÈ´Ù.

B. The second-best shear system is a web of diagonals at 45-deg angles.(The verticals or columns belong to the bending system and are not counted in the material volumn.) For this system, SRI=(5/8)*100=62.5. This system is used in the Erewhon Half-Mile Center to be shown next month.

C. ¶Ç´Ù¸¥ °¡»õ½Ã½ºÅÛÀº ´ë°¢¼± °¡»õ¿Í ¼öÆòÀ縦 È¥ÇÕÇÑ °ÍÀÌ´Ù. ÀÌ ½Ã½ºÅÛÀº ´õ ¸¹Àº Àç·á¸¦ »ç¿ëÇÏÁö¸¸, ½Ã°øÇϱ⿡´Â ´õ ½±´Ù. ¸¸¾à ´ë°¢¼± °¡»õÀÇ °æ»ç°¡

Á¦°ö±Ù(2/1)=1.414

À̶ó¸é Àü´Ü°­¼ºÁö¼ö´Â 100*(5/16)=31.3ÀÌ´Ù. ÀÌ Àü´Ü½Ã½ºÅÛÀº ½ÃƼÄß ¼¾ÅÍ, »ç¿ì½º¿þ½ºÆ® ÀºÇà¿¡¼­ »ç¿ëµÇ¾ú´Ù.

C. Another bracing system combines diagonals and horizontals. It uses more material but is easier to build. If the slope of the diagonals is

SQR(2/1)=1.414

the SRI=(5/16)*100=31.3. This system is used at Citicorp Center and the Bank of the Southwest.

°¡Àå ÀϹÝÀûÀÎ Àü´Ü½Ã½ºÅÛÀº °­Àý°ñÁ¶ÀÌ´Ù. Àü´Ü°­¼ºÁö¼ö¿¡ ÀÇÇØ ÃøÁ¤µÈ °ñÁ¶ÀÇ À¯È¿¼ºÀº ºÎÀçÀÇ ±æÀÌ¿Í ±íÀÌÀÇ Ýï¿¡ µû¶ó ´Ù¸£´Ù. ÇÙ½ÉÀûÀÎ Ýï´Â

P = ( H + L ) / D

ÀÌ´Ù.

D~G. D, E, F, G¶ó Ç¥½ÃµÈ ³× °³ÀÇ °ñÁ¶µéÀº ¸ðµÎ °°Àº °ª P=(H+L)/D=12¸¦ °®´Â´Ù. µû¶ó¼­ °°Àº Àü´Ü°­¼ºÁö¼ö¸¦ °°´Â´Ù. ö°ñ, ¿ÍÀ̵å Ç÷£Áö ´Ü¸éÀ¸·Î Áö¾îÁø °ñÁ¶ÀÇ °æ¿ì, Àü´Ü°­¼ºÁö¼ö´Â

SRI = 500/(P**2 + P + 4)

À̹ǷΠ¸ðµç ³× °³ÀÇ °ñÁ¶´Â °°Àº Àü´Ü°­¼ºÁö¼ö¸¦ °®´Â´Ù.

SRI = 500/(144 + 12 + 4) = 3.1

The most common shear systems are rigidly joined frames. The efficiency of a frame as measured by its SRI depends on the proportions of members' lengths and depths. The key proportion is :

P = ( H + L ) / D

The set of four frame labeled D, E, F, G all have the same value of

P=(H+L)/D=12

They therefore have the same SRI. For frames built from steel, wide-flange sections :

SRI = 500/(P**2 + P + 4)

All four frames have the same as :

SRI = 500/(144 + 12 + 4) = 3.1

H~K. (HºÎÅÍ K±îÁöÀÇ) °ñÁ¶µéÀº ºÎÀçÀÇ ±íÀÌ°¡ °°À¸¸ç P°ªÀº ¼­·Î ´Ù¸¥ °ªÀ» °®´Â´Ù. 36-ÀÎÄ¡ Çü°­ÀÇ °æ¿ì, ³× °³ÀÇ °ñÁ¶µéÀº Àç·áÀÇ ÃÑ ¹«°Ô´Â °°Áö¸¸ ³× ¹ø° °ñÁ¶°¡ óÀ½ÀÇ °ñÁ¶º¸´Ù ³× ¹è³ª °­¼ºÀÌ Å©´Ù. Á¤»ç¹æÇü °Ç¹° ¸ðµç ³× °³ÀÇ ¿Üº®¿¡ »ç¿ëµÈ ³× ¹ø° °ñÁ¶´Â ³ôÀº Àü´Ü°­¼ºÀ» °®°í ¶ÇÇÑ Àç·áÀÇ 2/3¸¦ ±âµÕ¿¡ »ç¿ëÇϴµ¥, ÀÌ ±âµÕµéÀº ÈǸ¢ÇÑ ÈڽýºÅÛÀ¸·Î¼­ ÀÛ¿ëÇØ ÀÌÁßÀÇ ¿ªÇÒÀ» ¼öÇàÇÒ ¼ö ÀÖ´Ù. °á°úÀûÀ¸·Î »ý±â´Â Çü»óÀº "Æ©ºê"¶ó°í ÀûÀýÇÏ°Ô ºÒ¸®¸ç, ¼¼°è¿¡¼­ °¡Àå ³ôÀº µÎ °³ÀÇ °Ç¹°ÀÎ ½Ã¾î½º Ÿ¿ö¿Í ¿ùµå Æ®·¹ÀÌµå ¼¾ÅÍÀÇ ±Ù°£ÀÌ µÇ¾ú´Ù.

Frames(H through K) have the same member depth D and varying values of P. With 36-in. steel sections, all four frames have essentially the identical total weight of material, but the fourth frame is more than four times as rigid as the first. A frame like the fourth used in all four exterior walls of a square building has high shear rigidity and also uses two-thirds of its material in columns, which are available to do double duty as a good bending system. The resulting configuration is properly called a "tube" and is the basis for the world's two tallest buildings : the Sears Tower and the World Trade Center.