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ุงู„ุณู„ุงู… ุนู„ูŠูƒู… ุงู„ูŠูˆู… ุณูˆู ู†ุชุญุฏุซ ุนู† ู…ูŠูƒุงู†ูŠูƒุง ุฃุณุทูˆุฑูŠุฉ
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32
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ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 32 ุญุฏุซ 33 ุญุฏุซ 33 ุญุฏุซ 33
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ุญุฏุซ 33 ุญุฏุซ 34 ุญุฏุซ 34 ุญุฏุซ 34 ุญุฏุซ 35 ุญุฏุซ 35 ุญุฏุซ 35
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ุญุฏุซ 35 ุญุฏุซ 35 ุญุฏุซ
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ู…ูƒุชุจ ุดูˆูŠู‡ ุงูŠู‡ ุงู„ูƒู„ุงู… ุงู„ู…ูุถู„ ุงูˆ ู‚ุฏ ูŠูƒูˆู† ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ ู…ูุถู„ ุงูˆ
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ู…ูุถู„ ุงูˆ ู…ูุถู„
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ุงูˆ ู…ูุถ
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frames and trusses ุงู„ frame ุงู„ู„ูŠ ู‡ูˆ ุงูŠุด ุงู„ ู‡ูŠูƒู„ ูˆ
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ุงู„ truss ุงู„ู„ูŠ ุนุงุฑููŠู†ู‡ ุงู„ู„ูŠ ุงุญู†ุง ุจู†ุณู…ูŠู‡ ุจุงู„ุนุงู…ูŠุฉ ุงู„
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truss ุงูŠุด ุงู„ truss ุงู„ุญูŠู† ู„ู…ุง ุงู†ุช ู…ุดูŠ ุงู†ุช ููŠ ู…ู…ุฑ
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ุงูŠุด ุจุชู„ุงู‚ูŠ ุงูˆ ุจู„ูƒูˆู† ุงูŠุด ุงู„ู„ูŠ ู‡ุง ุจูŠุณู…ูˆู‡ truss ุงู„ุงู†
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ุณู‚ู ุงู„ูƒุฑู…ูŠุฏ ุงู„ู„ูŠ ู‡ูˆ ุญุงุฌุฉ ุจู†ุณู…ูŠู‡ุง ุฏูŠ ุงู„ trussุงู„ู„ูŠ
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ู‡ูŠ ุงู„ุญู…ุงูŠุฉุŒ ู‡ู†ุชูƒู„ู… ุนู†ู‡ .. ูƒุดูุฉ ูŠุง ุงู†ุช .. ู„ุฃ ู„ุฃ ู…ุด
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ุงู„ูƒุดูุฉ .. ู‡ู‡ ุฏู‡ .. ู‡ู†ุชูƒู„ู… ุนู†ู‡ุงุŒ ู„ุงุชุฌู„ุฌูˆุด .. ุงู„ุขู†
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ู„ู…ุง ู†ุชูƒู„ู… ุนู„ู‰ ..
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Statically determinate structure when a structure
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member that is part of the structure is loaded in
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certain direction ูŠุนู†ูŠ ู„ู…ุง ูŠูƒูˆู† ุนู†ุฏู†ุง ุงู„ structure
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ู…ุญู…ู„ ุจุงุชุฌุงู‡ ู…ุนูŠู† ุงู„ load will cause reaction ูŠุนู†ูŠ
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ู„ูˆ ุฃุฌุช ู‚ูˆุฉ ุนู„ู‰ ุญุงุฌุฉ ู‡ูŠุตูŠุฑ ุงู„ู‡ูŠุด ุฑุฏุช ูุนู„ุงู„ุงู† ุฑุฏุฉ
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ุงู„ูุนู„ ู‡ุฐุง ูŠุนู†ูŠ ุงู† ุทุงู‚ุฉ ุฃุฎุฑู‰ ู…ุชุณุงูˆูŠุฉ ู„ู„ูˆุถุน ุณุชุนู…ู„ ููŠ
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ุงู„ุงุชุฌุงู‡ ุงู„ู…ุนูƒุณ ู„ูƒู„ ูุนู„ ุฑุฏ ูุนู„ ู…ุณุงูˆุก ููŠ ุงู„ู…ู‚ุฏุงุฑ
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ู…ุนูƒุณ ููŠ ุงู„ุงุชุฌุงู‡ ู‡ุฐุง ุงู„ู„ูŠ ุจูŠุญูƒูŠู†ุง ุงู† ู‡ูŠ ูƒูˆูŠุณ ุงู„
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reaction will counteract resist the load and stop
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the member from moving ูŠุนู†ูŠ ู‡ุฐู‡ ุงู„ู‚ูˆุฉ ู„ู…ุง ู†ูŠุฌูŠ
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ู†ุญุทู‡ุง ู…ุด ู‡ุชุฎู„ูŠ ุงู„ุฌุณู… ุฃูˆ ุงู„ุนุถูˆ ู‡ุฐุง ูŠุชุญุฑูƒwhen the
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loads and reactions acting in members are equal
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ู„ู…ุง ู‡ุฐุง ูŠูƒูˆู† ุงู„ุฃุญู…ุงู„ ูˆุฑุฏูˆุฏ ุงู„ุฃูุนุงู„ ุชุจุนุชู‡ุง ุฃูˆ
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ุงู„ุชูุงุนู„ ู…ุนู‡ุง ุงู„ู‚ูˆุฉ ุงู„ู…ุถุงุฏุฉ ู„ู‡ุง ู…ุชุณุงูˆูŠุฉุŒ ุฅูŠุด ุงู„ู„ูŠ
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ุจูŠุญุตู„ุŸ we say it is in equilibrium ุนู…ู„ูŠุฉ ุฅูŠุดุŸ
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ุงุชุฒูŠุงู†structures that are designed not to move to
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stay in equilibrium are called statically
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determined structures ูŠุนู†ูŠ ุงู„ู„ูŠ statically
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determined structure ู‡ู… ุงู„ structure in
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equilibrium ูŠุนู†ูŠ ุจุชุชุญุฑูƒุด ู„ุง ุจุฑูŠุญ ูˆู„ุง ุจุชุชุญุฑูƒ ุจุงู„ู‚ูˆุฉ
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ุงู„ู„ูŠ ุจุชู†ุถุบุท ุนู„ูŠู‡ ู‡ุฐุง ุจู†ู‚ูˆู„ ุนู†ู‡ ุฅูŠุดุŸ ุฃูŠูˆุฉ
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statically determined structure ูƒูˆูŠุณุŸ
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resultant forces and the center of gravity ุนุงุฏุฉ
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ุฃูŠ ู‡ูŠูƒู„ ุจูŠุญู…ู„
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ุฃุญู…ุงู„ ู…ุฎุชู„ูุฉููŠ ุณูˆุงุก ู…ู† ู†ุงุญูŠุฉ ุงู„ magnitude ุฃูˆ ู…ู†
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ู†ุงุญูŠุฉ ุงู„ุงุชุฌุงู‡ ุงู„ู„ูŠ ุจุชูŠุฌูŠ ุนู„ูŠู‡ to calculate the
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results of these different components ูู‡ุฐุง ุฎุฏุชูˆู‡ุง
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ุจุงู„ููŠุฒูŠุง component forces and engineer can
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calculate a resultant force or resultants ูŠุนู†ูŠ ููŠ
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ุงู„ุนุงุฏุฉ ุงุญู†ุง ูƒ .. ุฎุฏุชูˆู‡ุง ุจุงู„ statistics ููŠ ุงู„ุซุงู†ูˆูŠุฉ
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ุจุงู„ููŠุฒูŠุง ุตุญุŸููŠุฒูŠุง ุงู„ู ุฃุฎุฏุชู‡ุง ุงู†ุช ููŠ ุนู†ุฏูŠ ู‚ูˆุฉ
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ู…ุฎุชู„ูุฉ ุฌุงูŠ ุจุฏุฃ ุฃุฌูŠุจ ุงู„ู…ุญุตู„ุฉ ุชุจุนุชู‡ุง ุจุงุฌูŠุจ ุญุงุฌุฉ
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ุงุชุฌุงู‡ ุงู„ู…ุญุตู„ุฉ ููŠ ุงู„ุงุชุฌุงู‡ ุงู„ุนู…ูˆุฏูŠ ูˆุงู„ุนู…ูˆุฏูŠ ูˆุงู„ุฃูู‚ูŠ
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ูˆุจุนุฏูŠู† ุจุงุฌูŠุจ ุงู„ู…ุญุตู„ุฉ ุชุจุนุช ุงู„ุชู†ุชูŠู† ุชุทู„ุน ููŠ ุฃูŠ ุงุชุฌุงู‡
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ุจุณ ู„ุงุฒู… ุฃุญุฏุฏ ุงู„ู†ู‚ุทุฉ ุงู„ู„ูŠ ุนู†ุฏู‡ุง ุจุชุทู„ุงู‚ ูƒู„ ู‡ุฐู‡ ุงู„ู‚ูˆุฉ
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ุงู„ู„ูŠ ุจู†ู‚ูˆู„ ุงู„ center of gravity ุฃูˆ ุงู„ center ุงู„ู„ูŠ
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ุนู†ุฏูŠ ู„ู‡ุฐู‡ ุงู„ุดุบู„ุฉone of the main forces exerted in
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structure is gravity ุงุญู†ุง ููŠ ูƒู„ ุดูŠ ููŠ ุนู†ุฏู†ุง
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ุงู„ุฌุงุฐุจูŠุฉ ุงู„ุฃุฑุถูŠุฉ
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Okay ุงู„ gravity this acts vertically downward ุงู„ู„ูŠ
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ู‡ูŠ ูŠุนู†ูŠ ุนุงุฏุฉ ุงู„ gravity ุจุชูŠุฌูŠ ุฅูŠุด ุนู…ูˆุฏูŠ ููŠ ุงุชุฌุงู‡
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ุงู„ุฃุณูู„ ู‡ุฐู‡ ูˆ ุฏุงูŠู…ุง ู‡ุฐู‡ ุจู†ุญุณุจ ุญุณุงุจู‡ุง ุจุดูƒู„ .. ุจุฏูƒ
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ุชุดูˆู ุงู„ุชูุงุตูŠู„ ุจุชุฑูˆุญ ุนู„ู‰ ุงู„ chapter 9ุงู„ุฌุงุฐุจูŠุฉ ุชุชุนุฑุถ
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ู„ูƒู„ ุฏุฑู‘ุฉ ู„ุฌุงุฐุจู‡ุง ู„ูƒู„ ุฅุดูŠ ู„ูƒู„ ุฏุฑู‘ุฉ ู„ู‡ุง ุชุชุนุฑุถ
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ู„ู„ุฌุงุฐุจูŠุฉ However, to simplify their calculation
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engineers assumed that gravity exerted an
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imaginary point called the center of gravity ุงู„ุขู†
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ุงู„ center of gravity ุงู„ู„ูŠ ุจู†ุชูƒู„ู… ุนู„ูŠู‡ ู‡ูŠ ู†ู‚ุทุฉ ุฅูŠุด
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imaginary pointู‚ู†ุฏู‚ ู†ู‚ุทุฉ ูุฑุถูŠุฉ ุงุญู†ุง ุจู†ูุฑุถู‡ุง ู‡ูŠ ุนู„ู‰
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ุฃุฑุถ ุงู„ูˆุงู‚ุน ูƒู„ ุฌุฒุฆูŠุฉ ููŠ ุงู„ุฌุณู… ุฃูˆ ูƒู„ ุถุฑุฑ ุฅู„ู‡ุง ู‡ุฐู‡ ุจุณ
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ุงุญู†ุง ุจู†ู‚ูˆู„ ูƒูƒู„ ุจุฏู†ุง ู†ู‚ูˆู„ ู‡ูŠ ู‡ุฐู‡ ู†ู‚ุทุฉ ุงู„ุฌุงุฐุจูŠุฉ
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ุชุจุนุชู†ุง ุงู„ู„ูŠ ุจู†ุชูƒู„ู… ุนู†ู‡ุงDepending on the shape of
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the object, this point may be inside the object, a
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cross-sectional area or outside the cross
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-sectional area ูŠุนู†ูŠ ู…ู…ูƒู† ู†ู‚ุทุฉ ุงู„ุฌุงุฐุจูŠุฉ ุงู„ุฃุฑุถูŠุฉ
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ู‡ุฐู‡ ุงู„ู„ูŠ ุจู†ู‚ูˆู„ ุนู†ู‡ุง ุงูุชุฑุงุถูŠุฉ ุชุจู‚ู‰ ุฌูˆุง ุงู„ู…ุณุงุญุฉ
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ุงู„ุนุฑุถูŠุฉ ู„ู„ object ุฃูˆ ุชุจู‚ู‰ ุฎุงุฑุฌู‡ุง ูƒูƒู„ ุทุจ ูƒูŠู ุฏู‡
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ู‡ุชูƒูˆู† ุฎุงุฑุฌู‡ุงุŸ ุทุงู„ุน ุนู„ู‰ ุดูƒู„ู‡ุง ู‡ู†ุง ุจุณู‡ูˆู„ุฉ ุจู†ู‚ูˆู„ ูˆูŠู†
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ุฌุงูŠุฉุŸ ููŠ ุงู„ู†ุตู‡ู†ุง ุฌูˆุง ูˆู‡ู†ุง ุงุดุทู„ุนุช ุจุฑุง ูู‡ุฐู‡ ุจุชุนุทูŠูƒ
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example ูƒูŠู ุงู†ู‡ุง ู…ู…ูƒู† ุชูƒูˆู† ุจุฑุง ุงู„ุงู†
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ู„ู…ุง ู†ุชูƒู„ู… ุนู† ุงู„ frames and traces ุงู„ frame is made
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from a number of relative ten members ุนุงุฏุฉ ุงู„
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frame .. ุฎู„ูŠูƒู… ู…ุนุงูŠุง ูŠุง ุจู†ุงุชุงู„ู€ frame ู‡ูˆ ุนุจุงุฑุฉ ุนู†
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ุฅูŠุดุŸ ุทู„ุน ุฃู†ุช ุงู„ุญู…ุงูŠุฉ ุงู„ู„ูŠ ุจุชู†ุนู…ู„ ุนู„ู‰ ุงู„ุดุจุงูƒุŒ ู‡ุฐุง
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ุจู†ุณู…ูŠู‡ frame ุงู„ุฏุฑุฌุŒ ุดุงุญุท ุงู„ุญุฏูŠุฏ ุงู„ู„ูŠ ุนู„ู‰ ุดุงุญุท
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ุงู„ุฏุฑุฌุŒ ู‡ุฐุง ุจู†ุณู…ูŠู‡ frame ู‡ูˆ ุฅุทุงุฑุŒ ุจุชู‚ุฏุฑ ุชุนุชุจุฑูŠู‡ุŒ ุจุณ
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ุนุงุฏุฉ ุงู„ู…ู‚ุตุฏ ุงู„ู‡ู†ุฏุณูŠ ููŠู‡ ู‡ูˆ ุฅุทุงุฑ ู…ู† ุงู„ุฃุนุถุงุก ุชุจุนูŠู†ู‡ุŒ
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ุฅูŠุด ุจู†ู‚ูˆู„ ุนู†ู‡ ุงู„ู€ tinุŒ ุงุฑูุนุฉexample are bicycle
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frames ุงู„ุจุณูƒุงู„ูŠุช ุงู„ุฅุทุงุฑ ุชุจุนุช ุงู„ุจุณูƒุงู„ูŠุช steel frame
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building ุงู„ู„ูŠ ู‡ูŠ ุชุจุนุงุช ุงู„ุจู†ุงูŠุงุช members of a frame
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can form a complex shape often with many triangles
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called lattices ุงู„ุขู† ุนุงุฏุฉ ู„ูŠูƒูˆู† ุงู„ frame ู‚ูˆูŠ ุฅูŠุด
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ู„ุงุฒู… ุฃุนู…ู„ู‡ ุนู„ู‰ ุดูƒู„ ู…ุชู„ุชุงุช ู„ูˆ ุฃู†ุง ุฌูŠุช ุนู…ู„ุช frame
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ูƒุงู„ุชุงู„ูŠุฃุจู†ุงุก ุชู‚ู„ู‚ูˆุง ู…ุนุงู‡ ุจุฏูˆู† ุตูˆุช ุฌุงู†ุจูŠ ู‡ุฐุง
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frame ู„ูˆ ุฌูŠุช ุถุบุทุช ุนู„ูŠู‡ ุฅูŠุด ุงู„ frame ู‡ุฐุง ุจุฏูŠ ูŠุญุตู„
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ู„ู‡ุŸ ุจุณูˆู‚ุดุŒ ุจุงู„ุทุนุดุŒ ู…ุธุจูˆุท ู‡ุฐุง ุจูŠุตูŠุฑ .. ุจุชู„ุงู‚ูˆู‡ ุนู„ู‰
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ุทูˆู„ ุจูŠุญุตู„ุŒ ู…ุธุจูˆุทุŸ ู„ุฃุฏุนู…ู‡ ุฅูŠุด ุจุนู…ู„ุŸ ู„ูˆ ุญุทูŠุช ู…ูˆุชู„ุฉ
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ุชุงุนุช ู‡ู†ุง ุฅูŠุด ุจูŠุญุตู„ ู„ู‡ุŸ ุจุชุฌูˆู‰ู‡ุฐุง ุงู„ู‚ุตุฏ ููŠู‡ ุงู„ู„ูŠ
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ุนู†ุฏูŠุŒ ุงู„ุขู† ู‡ุฐู‡ ู‡ูŠ simple structureุŒ structure
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deformed under loadุŒ ู‡ู†ุง ุนู…ู„ุช ู„ุฅูŠุดุŸ adding cross
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members ุงู„ู„ูŠ ู‡ูŠ .. ุงู„ู„ูŠ .. ุงู„ู„ูŠ ู‡ูŠ ุงุณุชูู† ุฏู‡ ุฅูŠุดุŸ
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ุงู„ structure ุงู„ู„ูŠ .. ุงู„ู„ูŠ ู…ูˆุฌูˆุฏ ุนู†ุฏูƒ
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Okay members of the frame can form a complex shape
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often with many triangles called lattices ุงู„ู„ุงุชูŠุณ
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ู‡ุฐุง ู‡ูŠ ุงู„ triangular shape the advantage of
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triangles is that they are stiff ุงูŠุด ูŠุนู†ูŠ stiff
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ู„ู…ุง ุงู„ูˆุงุญุฏ stiff arm ุจุชู…ุฏูŠ ุงูŠุฏูƒ ุฒูŠ ู‡ูŠูƒูˆ ุจุช ..
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ุจุชู…ุดูŠ .. ุญุฏ ู…ู‚ุฏุฑ ูŠุฌุฑุจ ู…ู†ูƒุŸ ู‡ุฐุง ุจูŠุณู…ูŠู‡ุง stiff arm
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ู…ุดุฏูˆุฏุฉ ุงู„ aid ู…ุดุฏูˆุฏุฉ stiff armูู‡ุฏูˆู„ุฉ ุจูŠุนู…ู„ูˆุง
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ุงู„ุญุฏูŠุฏ stiff ูŠุนู†ูŠ ุฅูŠุดุŸ ุงู„ stiff arm ุชู†ุทุน ุฌูŠุด
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ู…ู…ุฏูˆุฏุฉ ู…ุดุฏูˆุฏุฉ ู…ุด ู…ุทุนูˆุฌุฉ ูู‡ูŠ ู„ู…ุง ุชุญุทูŠู‡ุง ุฒูŠ ู‡ูŠูƒุฉ ูˆ
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ุจุชุฒุฌูŠ ุญุฏ ู„ูˆ ูƒุงู†ุช ู…ุชู†ูŠุฉ ูˆ ุจุชุฒุฌูŠ ุญุฏ ู„ูˆ ููŠู‡ force
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ุจูŠุฌูŠุด ุจุงู„ุณูŠุงุฑุฉ ุชู†ุชู†ู‰ ุจุณ ู„ูˆ ูƒุงู†ุช ุฒูŠ ู‡ูŠูƒุฉ ู…ุงุญุฏุด
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ุงู„ุชุงู†ูŠุฉ ุตุนุจุฉ ูู‡ุฐู‡ ุงู„ููƒุฑุฉ ููŠ ุงู„ stiff they strongly
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resist deformation ูŠุนู†ูŠ ุชู‚ุฏุฑูŠุด ุงู„ุชุดูˆู‡ ุงู„ู„ูŠ ุนู†ุฏูƒ
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ุฃู†ุช ููŠ ุงู„ .. ููŠ ุงู„ู…ุนู†ู‰ .. ููŠ ุงู„ู…ุนู†ู‰ ุงู„ุณู„ุจูŠ .. ุฃู‡
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ุงุณุชูู‰ ุงู„ุดุฎุต ุงู„ู„ูŠ ุจุชู„ุงู‚ูŠู‡ ุฃุญูŠุงู†ุง ุจูŠู‚ูˆู„ ุนู†ู‡ ุงู„ู„ูŠ
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ุจูŠุบูŠุฑุดูŠุนู†ูŠ ู…ุฎ ูˆ ุจูƒู ุฒูŠ ู‡ูŠูƒ ุจุณ ููŠ ุงู„ .. ุจุฑุถู‡ ููŠ
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ุงู„ู„ุบุฉ ุงู„ุนุงู…ูŠุฉ ุงู„ู…ูˆุฌูˆุฏุฉ ุงู„ stiff ุฃูƒุชุฑ ุฃุดูŠ ุจูŠุณู…ูˆู‡ุง
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ุงู„ stiff arm ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ุงู„ุฅูŠุฏ ุงู„ู…ู…ุฏูˆุฏุฉ ุงู„ู„ูŠ ุจุชุฎู„ูŠ
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ู…ุณุงูุฉ ุจูŠู† ุงู„ุฃุดุฎุงุต ูุงู„ stiff ูŠุนู†ูŠ ุจุชุนู…ู„ุด ุฃู†ู‡ ูŠุนู†ูŠ
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ุฎู„ูŠู†ุง ู†ู‚ูˆู„ ูŠ lean ุจุช lean ุฃูˆ ุจุชุบูŠุฑุด ุดูƒู„ู‡ุง ู‡ุฐุง ุงู„
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..ุงู„ู„ูŠ ุจู†ุญูƒูŠ ููŠู‡ุง ุงู„ู€ triangular ุงู„ symbols can
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therefore be used to stiffen or brace a structure
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ูŠุนู†ูŠ ู„ุชู‚ูˆูŠ ุงู„ structure ุฃูˆ ู„ุชุฏุนู… ุงู„ structure ู‡ุฐุง
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ุงู„ู‡ุฏู ู…ู†ู‡ุง ุงู„ diagram two ุงู„ู„ูŠ ู‡ุชุดูˆููˆู‡ ุงู„
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structure ุฏูŠ ููˆู‚ ุงู„ู„ูŠ ุดูˆูู†ุงู‡ุง because the joints
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between the ten members are weak ุงู„ joints ุงู„ู„ูŠ ู‡ูŠ
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ุฅูŠุด ู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง jointุฃูŠูˆุฉ ู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง joints ู‡ุฏูˆู„
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ุงู„ joints ุงู„ุฑูƒุจ ูˆ ู‡ุฏูˆู„ ู‡ุฐู‡ ุงู„ู…ูุงุตู„ ู‡ูŠ ุงู„ู…ูุตู„
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ุงู„ู…ูุตู„ ุงู„ุฒูˆุงูŠุง ุชุนุฏ ุงูŠุด ู…ูุงุตู„ ุงู„ุชู‚ุงุก ุงูŠ ุฌุณู… ุงูŠ
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ุญุงุฌุชูŠู† ุจู†ุณู…ูŠู‡ุง ู…ูุตู„ ูุนู†ุง ู†ูˆุนูŠู† ู…ู† ุงู„ู…ูุงุตู„ ู…ูุงุตู„ ุฒูŠ
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ุงุญู†ุง ุงุฏูŠู†ุง ูˆ ุฑุฌู„ูŠู†ุง ู‡ุฏูˆู„ ุงูŠุด ุจู†ุณู…ูŠู‡ุง ู„ูŠู†ุฉ ุจุชุฎู„ูŠ
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ุญุฑูƒุฉูˆ ููŠ ู…ูุงุตู„ ู…ุด ู„ูŠู†ุง ุฒูŠ ุงู„ู…ูˆุฌูˆุฏ ู‡ู†ุง ู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง
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solid joints ูˆู‡ุฐู‡ ุจู†ุณู…ูŠู‡ุง pin joint ุงู„ pin joint
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ุงู„ู„ูŠ ู‡ูŠ flexible ููŠ flexibility ููŠู‡ุง ูˆู‡ุฐู‡ ู‡ู†ุชูƒู„ู…
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ุนู†ู‡ุง ูƒู…ุงู† ุณุงุทุฑูŠู†are weak and can flex easily flex
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ุฃูŠุด ูŠุนู†ูŠ ุจุชุชุญุฑูƒ ุจุณุฑุนุฉ joints which flex because
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they are weak or because they are designed to do
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so ุงู„ู„ูŠ ู‡ูŠ ู…ุตู…ู…ุฉ ุฒูŠ ุงู„ู…ูุงุตู„ ุงู„ุฅู†ุณุงู† ู…ุตู…ู…ุฉ ุงู†ู‡ุง
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ุชุชุญุฑูƒ ุชูƒูˆู† flexible are called bend joints ูุนุฑูุชูˆุง
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ุฅูŠุด ุงู„ bend jointsุŸุงู„ู„ูŠ ุจุชุชุญุฑูƒ ุงู„ุงู† ุงู„ู†ูˆุน ุงู„ุชุงู†ูŠ
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ู‡ูŠ lattices which are entirely bent joint and
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which therefore need cross members to stiffen them
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are called traces ุงู„ traces ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ุจุฏู‡ู… ุฏุนู…
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ุงู„ู€ trust contain two types of members, members
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that resist tension are called ties ููŠ ุนู†ุฏู‰ ุญุงุฌุงุช
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ุจู‚ุงูˆู… ุงู„ุดุฏ ุจู†ุณู…ูŠู‡ู… ties ูˆููŠ ุญุงุฌุงุช ุจุชู‚ุงูˆู… ุงู„ุงุดุงู„ู€
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compression ุงู„ู„ูŠ ุจุชู‚ุงูˆู… ุงู„ compression which
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members that resist compression are called struts
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ุงู„ู€ struts ุงู„ู„ูŠ ู‡ูŠ ุจุชู‚ุงุฑู† ุงู„ compression ุงู„ ties
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ุงู„ู„ูŠ ู‡ูŠ ุจุชู‚ุงุฑู† ุงู„ tension ุงู„ุดุฏ a joint which does
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not flex is called a rigid joint rigid ุงูˆ solid
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ุงู„ู„ูŠ ู‡ูŠ ุงูŠุด ุจุชุชุญุฑูƒุด or moments connectionrigid
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joints are often thick and securely joined for
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example by weld ุงูŠุด ุงู„ weld ู‚ู„ู†ุง ุนู†ู‡ุŸ
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ุงุชูƒู„ู…ู†ุง ุนู†ู‡ ุงู„ู…ุญุงุถุฑุฉ ู‚ุจู„ ุชู…ุงู†ูŠุฉ ูˆ ุนุดุฑูŠู† ู…ุธุจูˆุทุŸ
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ุงู„ุญุงู… ุนู…ู„ูŠุฉ ุงู„ุญุงู… ุงู„ู„ูŠ ู‡ูŠ ุงู„ weld ุงู„ุขู† ุงุชุทู„ุน ุนู†ุฏู‰
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ุชุชุฐูƒุฑูˆุง ุณุฌูˆู ุงู„ูƒุฑู…ูŠุฏุŸ ุดูุชูˆู‡ู… ุงูŠุด ุงู„ุดูƒู„ ุชุจุน ุงู„ุญุงู…
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ุงู„ู„ูŠ ุชุจุนู‡ุŸ ุฒูŠ ู‡ูŠูƒ ู…ุธุจูˆุทุŸุงู„ุงู† ู„ูˆ ุถุบุทุช ู‡ุฐู‡ joint
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ุจู†ุณู…ูŠู‡ุง pin joint ู„ูˆ ุถุบุทุช ุนู„ูŠู‡ุง ุงูŠุด ุจูŠุญุตู„ ู„ู‡ ู‡ุฏูˆู„
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ู‡ุฏูˆู„ุฉ ุจุฏู‡ุง ุชูุฑุฏ ุงูˆ ู‡ุฏูˆู„ุฉ ุงูŠุด ุจุฏู‡ู… ูŠุณูˆูˆุง ุงู„ุงู† ู„ูˆ
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ุฑุจุทุชู‡ู… ุจุญุงุฌุฉ ู…ู† ู‡ู†ุง ุญุทูŠุช ุดูƒูุฉ ุฎุดุจ ุงูˆ ุญุงุฌุฉ ุจู‡ุฐู‡ ู‡ุฐูŠ
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ุจุณู…ูŠู‡ุง ุงู„ู„ูŠ ุดูุชูˆู‡ุง ุงูŠุด ูŠู‚ูˆู„ูˆุง ุงุญู†ุง ุนู†ุฏู†ุง straw
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ู‡ุฏูˆู„
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ู‡ุฐุง ูƒู„ู‡ ุจู†ุณู…ูŠู‡ trust ูˆู‡ุฐู‡ ุงู„ู„ูŠ ุจู†ุณู…ูŠู‡ุง ุงู„ tie ุทู„ุน
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ุนู„ู‰ ุญุงุฌุฉ ุชุงู†ูŠุฉุŒ ู„ูˆ ุฌูŠุจุช ู‡ุฐู‡ ูƒู„ู‡ุง ู…ูˆุฌูˆุฏุฉ ุนู†ุฏู†ุง ุงู„
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raft ุชุจุน ุงู„ูƒุชุจุŒ ู…ุธุจูˆุทุŸ ุงู„ raft ุชุจุน ุงู„ูƒุชุจุŒ ุฅูŠุด
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ุจูŠุญุตู„ ู„ู‡ุŸ ู‡ุฐุง ู„ูˆ ุญุทูŠุช ุงู„ูƒุชุจ ุนู„ู‰ ู‡ุฐุงุŒ ุฅูŠุด ุจูŠุญุตู„
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ู„ู‡ุฐุงุŸ ุชู†ุทุนุฌุŒ
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ุจุธุจุทุŸู…ุด ู‡ุฐู‡ ุจุฏู‡ุง ุชู†ุทุนุดุŸ ุงู„ุงู†
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ุทุจูŠุนูŠ ู„ูˆ ุงู†ุช ุฌุจุช ุญุงุฌุฉ ู…ุด ุฌุงูˆูŠุฉ ูŠุนู†ูŠ ู…ู…ูƒู† ุทุงูˆู„ุงุช
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ุงู„ูƒู…ุจูŠูˆุชุฑ ุงู„ู„ูŠ ุจุชุดูˆููˆู‡ุง ุจุชู†ุจูŠุน ููŠ ุงู„ุณูˆู‚ ุงู„ุชุฌุงุฑูŠ
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ู‡ุฐู‡ good examples ู…ุธุจูˆุท ุชุทู„ุน ุนู„ูŠู‡ุง ุจุชู„ุงู‚ูŠ ู‡ุฐู‡ ุนู„ู‰
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ุทูˆู„ ุจุชู†ุทุนุด ุงูŠุด ุจูŠุนู…ู„ูˆุงุŸ ุจุฑุจุทูˆุง ุญุงุฌุฉ ู‡ู†ุง ู„ูˆ ูƒุงู†ุช
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ู‡ุฐู‡ ุงุฑุชุจุทุช ู…ู† ููˆู‚ ู‡ุฐุง ุจุณู…ูŠู‡ tie ู„ูŠุดุŸู„ุฃู† ู‡ุฐุง ุจูŠู‚ุงูˆู…
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ู„ู„ุดุฏ ูˆู‡ุฐุง ุจูŠุจู‚ู‰ ุงูŠุดุŸ ุจุงู„ู‚ูˆุงู… ุงู„ู„ูŠ ููŠ ุงู„ุฏุงุฎู„ุŒ ุงูŠูˆุฉุŒ
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ู‡ุฐุง ุงู„ู€strap ุงู„ุขู† ู„ูˆ ุญุทูŠุช ู‡ุงุฌุฉ ุชุงู†ูŠุฉ ุฒูŠ ู‡ุฐู‡
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ูˆุญุทูŠุชู‡ุง ุนู„ู‰ ุงู„ู„ูŠ ุนู†ุฏูŠ ุชุญุชุŒ ุงูŠุด ู‡ุฐู‡ ุตุงุฑุชุŸ ู‡ุฐู‡
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ุงู„ู€strap ูˆู‡ุฐู‡ ุงู„ู€tie ู‡ุฐุง ุงู„ frame ุงู„ุขู†ุŒ ู‡ุฐู‡ ุงู„ุดุฌุฉ
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ุฅูŠุด ุจูŠุญุตู„ ู„ู‡ุงุŸ ู‡ุฐุฉ will get compressed ู„ูˆ ุจู‚ู‰
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ุงู„ูˆุฒู†ุŒ ู‡ุชู†ุถุบุทุŒ ู‡ุฐู‡ ุงู„ุดุฌุฉ ุงู„ุชุงู†ูŠุฉ ุงู„ู„ูŠ ุจุฑุง ุฅูŠุด
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ุจูŠุตูŠุฑ ู„ู‡ุงุŸ ุชู†ุดุฏู…ุธุจูˆุท ู‡ุฐู‡ ู‡ุชุตุจุญ tension ู‡ุงู† ู„ูˆ ุญุทูŠุช
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ู‡ุฐู‡ ุงู„ุดูƒู„ ู‡ุงู† ู‡ุงู† ุนู†ุฏูŠ tension ูˆ ู‡ุงู† ุนู†ุฏูŠ
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compression ู†ูˆุน
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ุงู„ู‚ูˆุฉ ู‡ุฐู‡ ุจุฏู‡ุง ุชุถุบุท ุงู„ู„ูŠ ู‡ุงู† ูˆู‡ุฐุง ุจุฏู‡ุง ุชุณูˆูŠ ุงู„ู„ูŠ
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ู…ูˆุฌูˆุฏ ู‡ุงู† ู‚ูˆู„ู†ุง ุงู„ tie ูˆ ู‡ุงู† ุงูŠุด ูˆ ู‡ุงู† ุงู„ strutูƒูƒู„
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ู‡ุฐุง ุนู„ู‰ ุจุนุถู‡ ุจู†ุณู…ูŠู‡ ุฅูŠุด ุงู„ trust ุฃูˆ ุงู„ frame ูƒูˆูŠุณุŸ
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ุทูŠุจ
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ู†ูŠุฌูŠ ุงู„ุขู† complete the explanation using words and
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expression from a ุงู„ุฃูˆู„ ูู‚ุฑุฉ you will need to
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change the form of one wordุงู„ุงู† ุงู†ุง ุญุงุทุท ู„ู‡ุง ุฃุฌูˆุจุฉ
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ู…ุด ุญุงุทุท ู„ู‡ุง ุณูˆุงุก ุนู„ู‰ ุทูˆู„ ู‡ุฐุง ุงู„ู…ูุฑูˆุถ ุญุงุทูŠุช ู„ู‡ุง
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ุญุฑูƒุฉ ุนุดุงู† ุชุฎุชู„ูŠ and it's statically determined
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structure each load acting on this structure is
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ุฅูŠุดุŸ ูˆู‡ูŠ ู…ูˆุฌูˆุฏุฉ counteracted ุฃุธุจุท counteracted by
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ุฅูŠุดุŸa reaction ุงู„ุงู† ุนู†ุฏูŠ statically determinate
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ุงูŠุด ูŠู‚ูˆู„ู†ุง ุงู„ statically determinate ู†ุนูŠุฏ ุนู„ูŠู‡ุง
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ุชุฃูƒูŠุฏ ุนุดุงู† ุฃุฌูŠ ูˆ ู…ุชุฃุฎุฑ ุงู„ statically determinate
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structure ุงู„ู„ูŠ ู‡ูˆ ุงู„ structure is in equilibrium
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and does not move ู…ุธุจูˆุท ุงู„ุงู† ุงู„ equilibrium ุงูŠุด
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ุนู†ุฏูŠ ุนู†ุฏูŠ load ุงูˆ forces ูˆ ููŠ ุนู†ุฏูŠ counter forceุฃูˆ
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load ุนู†ุฏู‡ุง ู„ู…ุง ุงุชู†ูŠู† ูŠุจู‚ูˆุง ู…ุชุณุงูˆูŠูŠู† ูˆู…ุชุนุงูƒุณูŠู† ููŠ
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ุงู„ุงุชุฌุงู‡ in opposite direction equally in the
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magnitude is equal and the direction is opposite
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ู‡ุฐุง ุจู†ู‚ูˆู„ it's under equilibrium ุงู„ู„ูŠ ู‡ูŠ ููŠ ู…ุฑุญู„ุฉ
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ุงุชุฒุงู† ู‡ุฐุง ุงู„ู„ูŠ ุจู†ุญูƒูŠ ุนู†ู‡ this means the structure
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always remain in equilibrium
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ุงู„ุงู† ุงุชุทู„ุน ุนู†ุฏู‰ ู‡ู†ุง ุงูŠุด ู…ูˆุฌูˆุฏ ุนู†ุฏู‰ุŸ ู‡ู‰ ุงู„ trust
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ุงู„ู„ู‰ ู…ูˆุฌูˆุฏ ุนู†ุฏู‰ ู‡ู†ุง ุงูŠุด ุนู†ุฏู‰ุŸ forces ู„ูˆ ุญุทูŠุช ู…ุซู„ุง
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ู‡ู†ุง ู„ุบุงูŠุฉ loads from three supports carrying a
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large satellite dish ู‡ุฏูˆู„ ุงู„ forces ุฌุงูŠ ู…ู† ุชู„ุงุช
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ุงู…ุงูƒู†ู…ุญู…ูˆู„ ุนู„ูŠู‡ู… satellite dish ูŠุนู†ูŠ ู‡ุงุฏ ุฌุงูŠ ุนู„ู‰
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00:18:39,520 --> 00:18:43,500
ูˆูŠู†ุŸ ุนู„ู‰ ุงู„ุณุทุญ ุงู„ู„ูŠ ู‡ุงุฏ ุงู„ุงู† ู†ู‚ุทุฉ ุงู„ result sense
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ุชุจุนู‡ู… ูˆูŠู†ุŸ ู‡ุงุฏ ุชูƒูˆู† ู‡ุงุฏ ุงู„ุงู† ู‡ุฐุง ุจู†ู‚ูˆู„ to analyze
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ุฏุฑูˆู structure shown in diagram one and engineer
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draw diagram two ุงู„ุงู† diagram two for analysis
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purposes ูŠุนู†ูŠ ู„ู‡ุฏู ุงู„ุชุญู„ูŠู„ to help make some
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initial simple calculationIn diagram two, the
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engineer uses the following assumption and
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information The three component forces from
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loads
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act as a singleresultants ู…ุญุตู„ุฉ ู…ุธุจูˆุท ููŠ ุงู„
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diagram ุงุชู†ูŠู† ู‡ุฐู‡ ุตุงุฑุช ุชู„ุงุชุฉ ูˆุงุญุฏุฉ ูƒูŠู ุจุนู…ู„ู‡ู… ุจุฌูŠุจ
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ุงู„ู…ุญุตู„ุฉ ุชุจุนุชู‡ู… resultant force in the top of the
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frame all joints in the frame are ุงูŠุด ุณู…ู†ุงู‡ู… ู‡ุฏูˆู„
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ุงู„ joints ู‡ุฏูˆู„ุฉ flexible ูˆู„ุง rigid flexible ู„ูˆ ุงู†ุง
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ุถุบุท ุนู„ูŠู‡ู… ุจุชุญุฑูƒูˆุง ู…ุธุจูˆุทููŠ ู‡ุฏู ู†ุณู…ูŠู‡ ุฅูŠุดุŸ pin
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joints ุงู„ joints ู‚ู„ู†ุง ุงู„ู…ูุตู„ ุงู„ pin ุงู„ู„ูŠ ู‡ูŠ ู…ูุตู„
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flexible flexible joints can flex so the frame
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behaves as ุฅูŠุด ู‚ู„ู†ุงุŸtruss ู…ุธุจูˆุท ุงู„ุงู† ุงู„ู„ูŠ ู‚ู„ู†ุง ุงู„
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trust ุงู„ู„ูŠ ู‡ูˆ ุฅูŠุด ุนู†ุฏูŠ frame with flexible joint
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ุฃูˆ pin joint ู…ุด rigid ุงู„ู„ูŠ ุนู†ุฏูŠ ุฏูŠ ุฅูŠุด of ุฏุฑูˆู
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structure ุญุงุฌุฉ ู…ู† ุชู„ุช ูƒู„ู…ุงุช the center of a
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gravity of ุฏุฑูˆู structure shown in redุงู„ู„ูŠ ุงู†ุชูˆุง
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ุดุงูŠููŠู†ู‡ ู‡ู†ุง not including the satellite dish is
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exactly halfway between the two supports ูŠุนู†ูŠ ุงู„ู„ูŠ
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ู‡ูŠ ููŠ ุงู„ู†ุต ุฃุฌุง ู‡ุงูŠ
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ุงู„ุฎู…ุณุฉ ุงู„ุงู† in diagram two which of the members
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are ties and which are struts ุงู„ู„ูŠ ู‡ู†ุง ุงู„ a ู‡ุฐูŠ
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00:21:02,140 --> 00:21:10,040
ุงูŠุด ู‡ูŠ ู‡ุฐูŠStraight ู‡ุฏู‰ Straight ู‡ุฏู‰ Tie ู‡ุฏูˆู„
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ุงู„ุดุบู„ุงุช ุจุฏูƒูˆุง ุชุนุฑููˆู‡ุง ู„ุฃู† ู‡ุฏู‰ ู…ู† ุงู„ุดุบู„ุงุช ุงู„ุณู‡ู„ุฉ
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ุทูŠุจ choose the correct word from the bracket to
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00:21:21,080 --> 00:21:25,280
complete the sentences ุจุฏู†ุง ุงู„ูƒู„ู…ุฉ ุงู„ุตุญู‰ traces
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00:21:25,280 --> 00:21:32,700
are frameworks or ties ุงูŠุด ุงู„ trace framework with
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00:21:32,700 --> 00:21:39,810
ุงูŠุดู‚ูˆู„ ู„ูˆ ุฏูŠ flexible ุฃูˆ joint ุฃูˆ pin jointsุŒ
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ู…ุธุจูˆุทุŸ ุทูŠุจ ุงู„ connection between members which
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00:21:43,850 --> 00:21:50,190
flexes is calledุŸ pin joint ู…ุด rigidุŒ ูƒูˆูŠุณุŸ Struts
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are designed to resist compression ูˆู„ุง tensionุŸ
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compression ุทู„ุน ุนู†ุฏ ุงู„ tie ุฅูŠุดุŸ ุงู„ tie ุงู„ู„ูŠ ู‡ูŠ
256
00:22:00,530 --> 00:22:06,010
ุนู…ู„ูŠุฉ ุงู„ ุฅูŠุดุŸ ุงู„ tensionุŒ ุฃูŠูˆุฉู‡ุฐู‡ ุนู…ู„ูŠุฉ ุงู„ tension
257
00:22:06,010 --> 00:22:11,430
ุจู†ุณู…ูŠู‡ุง ุงู„ tie ูˆ ุงู„ compression ุงู„ stress ูˆ ุงู„
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trust ุงู„ู„ูŠ ู‡ูˆ ุจูŠุญู…ู„ ุงู„ุชู†ุชูŠู† ูƒูˆูŠุณ by adding cross
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member frames is embraced ูˆ ู„ุง being joined making
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it stiffer embraced embraced ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ู‚ู„ู†ุง ุนู†ู‡ุง
261
00:22:25,010 --> 00:22:33,790
embraced ุงู„ู„ูŠ ู‡ูŠ ู„ู…ุง ู†ู‚ูˆู„ ุนู†ู‡ ุฅูŠุด ุจูŠุนู…ู„ู„ู†ุงstiffen
262
00:22:33,790 --> 00:22:43,050
ูˆ brace ู†ูุณ ุงู„ุดูŠุก ู„ู…ุง ู†ุนู…ู„ ุงู„ stiffen ู‡ุงูŠ ุทูŠุจ ุงู„ุขู†
263
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ุฏู‡ ุจู†ุทู„ุน ุงุญู†ุง ุงูŠุด ุงู„ู„ูŠ ู…ุฑู† ุนู„ูŠู†ุง ุงู„ูƒู„ู…ุงุช ููŠ ู‡ู†ุง
264
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ุงุชูƒู„ู…ู†ุง ููŠ ุงู„ chapter ู‡ุงูŠ ุนู„ู‰ ุงู„ structural
265
00:22:52,750 --> 00:22:59,100
mechanicsุชูƒู„ู…ู†ุง ููŠู‡ ุนู„ู‰ .. ุฃูˆู„ุง ู‚ู„ู†ุง ู„ู…ุง ุงู„ frame
266
00:22:59,100 --> 00:23:04,820
ุงู„ู„ูŠ ุนู†ุฏูŠ is statically determinant structure ุฅูŠุด
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ู…ุนู†ุงุชู‡ุŸ ุงู„ structure is under equilibrium and not
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moving ุทุจ ู„ู…ุง ูŠูƒูˆู† under equilibrium ุฅูŠุด ุงู„ู„ูŠ
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00:23:13,440 --> 00:23:17,600
ุนู†ุฏูŠุŸ ุนู†ุฏูŠ two different forces ุฃูˆ two different
270
00:23:17,600 --> 00:23:23,850
loadsof equal magnitude and opposite direction act
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00:23:23,850 --> 00:23:29,390
ุนู„ู‰ ุงู„ frame ุงู„ู…ูˆุฌูˆุฏ ู‡ู†ุง ุงู„ุฃู† ุงุชูƒู„ู…ู†ุง ุจุฑุถู‡ ุนู„ู‰
272
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ุญุงุฌุฉ ุชุงู†ูŠุฉ ุจุนุฏู‡ุง ู‡ุฐุง ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ุฌุฒุฆูŠุฉ ู‡ุฐู‡ุงู„
273
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gravity ูˆ ุงู„ center of gravity ุงู„ gravity ู‡ูŠ ุงุญุฏู‰
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ุงู„ forces ุจุชุฃุซุฑ ุนู„ู‰ ูƒู„ ุดูŠุก ูˆ ุฏุงูŠู…ุง ุงุญู†ุง ุจุชูƒูˆู†
275
00:23:43,790 --> 00:23:47,950
downward ูˆ ู…ู…ูƒู† ุงู†ุชูˆุง ุจุชุนุฑููˆู‡ุง ูƒูŠู ุชุญุณุจูˆู‡ุง ุงู„ู„ูŠ ู‡ูŠ
276
00:23:47,950 --> 00:23:53,030
ุจุชุณุงูˆูŠ M ููŠ G ู…ุธุจูˆุทุŸ ุงู‚ูˆู„ูƒูˆุง ููŠ ุงู„ููŠุฒูŠุงุก ู…ุฑุช
277
00:23:53,030 --> 00:23:58,310
ุนู„ูŠูƒูˆุง ุงู„ G ุงู„ู„ูŠ ู‡ูŠ A ุงู„ A ุงู„ู„ูŠ ู‡ูŠ ุจุณ ููŠ ุงู„ .. ููŠ
278
00:23:58,310 --> 00:24:04,180
ุงู„ gravity ูƒุฏู‡ุด ุจุชุณุงูˆูŠุŸุชุณุนุฉ point ุชู…ุงู†ูŠุฉ ูˆุงุญุฏ
279
00:24:04,180 --> 00:24:08,160
meter squared per second ู…ุธุจูˆุท ุงูˆ meter per second
280
00:24:08,160 --> 00:24:12,520
squared ุงู„ุงู† ุงู„ู„ูŠ ุนู†ุฏูŠ ู‡ุฐู‡ ุงู„ู„ูŠ ุจู†ุชุทู„ุน ุนู„ูŠู‡ุง ุงู„ุงู†
281
00:24:12,520 --> 00:24:18,520
ู„ู…ุง ู†ูŠุฌูŠ ุจุนุฏ ู‡ูŠูƒ ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ structure with
282
00:24:18,520 --> 00:24:22,280
different joint ู‚ูˆู„ู†ุง ุงู„ joints ู„ู…ุง ุชูƒูˆู† flexible
283
00:24:22,280 --> 00:24:27,780
ุจู†ุณู…ูŠู‡ุง pin joint ูˆ ู„ู…ุง ุชุจู‚ู‰ hard ุงูˆ solid ุจู†ุณู…ูŠู‡ุง
284
00:24:27,780 --> 00:24:33,000
ุงูŠุด rigid jointsุงู„ุงู† ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ structure ุชุจุนู‡
285
00:24:33,000 --> 00:24:37,440
ุฏู‡ ุงู„ structure ุงู„ู…ูˆุฌูˆุฏ ุนู†ุฏู‰ with flexible ุงูˆ ุจูŠู†
286
00:24:37,440 --> 00:24:43,680
joint ุณู…ู†ุงู‡ traces ุงูˆ trace ุงู„ุงู† ุงู„ู„ู‰ ุนู†ุฏู‰ ููŠ ุงู„
287
00:24:43,680 --> 00:24:48,940
trace ุนู†ุฏู‰ ููŠู‡ member ุฏู‡ ุงู„ member members resist
288
00:24:48,940 --> 00:24:53,840
compression ุณู…ู†ุงู‡ู… ุงูŠุดุŸ stress ูˆ ุฏู‡ ุนู…ู„ูˆุง
289
00:24:53,840 --> 00:25:00,670
resisting ู„ู„ tension ุณู…ู†ุงู‡ู… ุงูŠุดุŸ tieู‡ูƒุฐุง ุฎู„ุตู†ุง