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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
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ุ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
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ุญุฏุซ 35 ุญุฏุซ 35
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ู…ุด ุดูˆูŠู‡ ุงูŠู‡ ุงู„ูƒู„ุงู… ุงู„ู…ูุถู„ ุฃูˆ ู‚ุฏ ูŠูƒูˆู† ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ ู…ูุถู„ ุฃูˆ
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ู…ูุถู„ ุฃูˆ ู…ูุถู„
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ุฃูˆ ู…ูุถู„
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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 ุฃูˆ ุจู„ูƒูˆู† ุงูŠุด ุงู„ู„ูŠ ู‡ุง ุจูŠุณู…ูˆู‡ truss ุงู„ุขู†
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ุณู‚ู ุงู„ูƒุฑู…ูŠุฏ ุงู„ู„ูŠ ู‡ูˆ ุญุงุฌุฉ ุจู†ุณู…ูŠู‡ุง ุฏูŠ ุงู„ู€ truss ุงู„ู„ู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„ุฌู„ูˆุด .. ุ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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a 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 ู„ู‡ุง ุฑุฏ ูุนู„ ุงู„ุขู† ุ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„ ู…ุณุงูˆู ูู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 ูŠุชุญุฑูƒ when 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 ุงูŠุด ุงู„ู„ูŠ
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ุจูŠุญุตู„ุŸ we say it is in equilibrium ุนู…ู„ูŠุฉ ุงูŠุดุŸ
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ุงุชุฒุงู† 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†ู‡ ุงูŠุดุŸ ุ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„ูุฉ ูู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„ููŠุฒูŠุงุก 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„ููŠุฒูŠุงุก ุตุญุŸ ููŠุฒูŠุงุก ุ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„ุฉ one 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 ุงูŠุด ุ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 ุงูŠุด
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imaginary point ู†ู‚ุ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†ู‡ุง Depending 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„ุขู†
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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†ุงุช ุงู„ู€ frame ู‡ูˆ ุนุจุงุฑุฉ ุนู†
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ุงูŠุดุŸ ุ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 ุชุจุนุฉุŒ
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ุงูŠุด ุจู†ู‚ูˆู„ ุนู†ู‡ ุงู„ู€ tinุŒ ุงุฑูุนุฉ example 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 ุงูŠุด
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ู„ุงุฒู… ุฃุนู…ู„ู‡ ุนู„ู‰ ุดูƒู„ ู…ุชู„ุชุงุช ู„ูˆ ุฃู†ุง ุฌูŠุช ุนู…ู„ุช frame
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ูƒุงู„ุชุงู„ูŠ ุฃุจู†ุงุก ุชู‚ู„ู‚ูˆุง ู…ุนุงู‡ ุจุฏูˆู† ุตูˆุช ุฌุงู†ุจูŠ ู‡ุฐุง
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frame ู„ูˆ ุฌูŠุช ุถุบุทุช ุนู„ูŠู‡ ุงูŠุด ุ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…ู‡ ุงูŠุด ุจุนู…ู„ุŸ ู„ูˆ ุญุทูŠุช ู…ูˆุชู„ุฉ
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ุชุงุนุช ู‡ู†ุง ุงูŠุด ุ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‡ ุงูŠุดุŸ
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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 ู‡ูŠูƒ ูˆุจุช ..
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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 arm ูู‡ุฐูˆู„ุฉ ุจูŠุนู…ู„ูˆุง
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ุงู„ุญุฏูŠุฏ stiff ูŠุนู†ูŠ ุงูŠุดุŸ ุงู„ู€ stiff arm ุชู†ุทุน ุฌูŠุด
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ู…ู…ุฏูˆุฏุฉ ู…ุดุฏูˆุฏุฉ ู…ุด ู…ุทุนูˆุฌุฉ ูู‡ูŠ ู„ู…ุง ุชุญุทูŠู‡ุง ุฒูŠ ู‡ูŠูƒ ู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 ู‡ูŠูƒ ู…ุ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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ุงู†ุช ููŠ ุงู„ู€ .. ููŠ ุงู„ู…ุนู†ู‰ .. ููŠ ุงู„ู…ุนู†ู‰ ุงู„ุณู„ุจูŠ .. ุงู‡
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ุงุณุชูู‰ ุงู„ุดุฎุต ุงู„ู„ูŠ ุจุชู„ุงู‚ูŠู‡ ุฃุญูŠุงู†ุง ุจูŠู‚ูˆู„ ุนู†ู‡ ุงู„ู„ูŠ
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ุจูŠุบูŠุฑุด ูŠุนู†ู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 ุดูŠุก ุจูŠุณู…ูˆู‡ุง
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ุงู„ู€ stiff arm ุงู„ู„ูŠ ู‡ูŠ ุงูŠุด ุงู„ุฅูŠุฏ ุงู„ู…ู…ุฏูˆุฏุฉ ุงู„ู„ูŠ ุจุชุฎู„ูŠ
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ู…ุณุงูุฉ ุจูŠู† ุงู„ุฃุดุฎุงุต ูุงู„ู€ stiff ูŠุนู†ูŠ ุจุชุนู…ู„ุด ุงู†ู‡ ูŠุนู†ูŠ
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ุฎู„ูŠู†ุง ู†ู‚ูˆู„ ุจุชู€ lean ุจุชู€ 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 jointุŸ ุฃูŠูˆุฉ ู‡ุ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 ุฅูŠุดุŸ ู…ูุงุตู„ ุงู„ุชู‚ุงุก ุฃูŠ ุฌุณู… ุฃูŠ
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ุญุงุฌุชูŠู† ุจู†ุณู…ูŠู‡ุง ู…ูุตู„ ูุนู†ุง ู†ูˆุนูŠู† ู…ู† ุงู„ู…ูุงุตู„ ู…ูุงุตู„ ุฒูŠ
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ุฅุญู†ุง ุฅูŠุฏูŠู†ุง ูˆ ุฑุฌู„ูŠู†ุง ู‡ุฏูˆู„ ุฅูŠุด ุจู†ุณู…ูŠู‡ุงุŸ ู„ูŠู†ุฉ ุจุชุฎู„ูŠ
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ุญุฑูƒุฉ ูˆ ููŠ ู…ูุงุตู„ ู…ุด ู„ูŠู†ุฉ ุ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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ุฅูŠุด ู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 ุฅู†ู‘ู‡ุง
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ุชุชุญุฑูƒ ุชูƒูˆู† flexible are called bend joints ูุนุฑูุชูˆุง
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ุฅูŠุด ุงู„ bend jointsุŸ ุงู„ู„ูŠ ุจุชุชุญุฑูƒ ุงู„ุขู† ุงู„ู†ูˆุน ุงู„ุซุงู†ู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 ุฅูŠุดุŸ ุ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†ุฏูŠ ุญุงุฌุงุช
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ุจุชู‚ุ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 ุฃูˆ solid
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ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุดุŸ ุจุชุชุญุฑูƒุด or moments connection rigid
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joints are often thick and securely joined for
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example by weld ุฅูŠุด ุ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† ุฅุทู„ุน ุนู†ุฏูŠ
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ุชุชุฐูƒุฑูˆุง ุณุฌูˆู ุงู„ูƒุฑู…ูŠุฏุŸ ุดูุชูˆู‡ู… ุฅูŠุด ุงู„ุดูƒู„ ุชุจุน ุงู„ุญุงู…
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ุงู„ู„ูŠ ุชุจุนู‡ุŸ ุฒูŠ ู‡ูŠูƒ ู…ุธุจูˆุทุŸ ุงู„ุขู† ู„ูˆ ุถุบุทุช ู‡ุฐู‡ joint
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ุจู†ุณู…ูŠู‡ุง pin joint ู„ูˆ ุถุบุทุช ุนู„ูŠู‡ุง ุฅูŠุด ุจูŠุญุตู„ ู„ู‡ ู‡ุฏูˆู„
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ู‡ุฏูˆู„ุฉ ุจุฏู‡ุง ุชูุฑุฏ ุฃูˆ ู‡ุฏูˆู„ุฉ ุฅูŠุด ุจุฏู‡ู… ูŠุณูˆูˆุงุŸ ุงู„ุขู† ู„ูˆ
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ุฑุจุทุชู‡ู… ุจุญุงุฌุฉ ู…ู† ู‡ู†ุง ุญุทูŠุช ุดููƒูุฉ ุฎุดุจ ุฃูˆ ุญุงุฌุฉ ุจู‡ุฐู‡ ู‡ุฐูŠ
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ุจูุณู…ู‘ูŠู‡ุง ุงู„ู„ูŠ ุดูุชูˆู‡ุง ุฅูŠุด ูŠู‚ูˆู„ูˆุงุŸ ุฅุญู†ุ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 ุซุงู†ู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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ุจุธุจุทุŸ ู…ุด ู‡ุฐู‡ ุจุฏู‡ุง ุชู†ุทุนุดุŸ ุงู„ุขู†
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ุทุจูŠุนูŠ ู„ูˆ ุฃู†ุ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 ุฅูŠุด ุจูŠุนู…ู„ูˆุงุŸ ุจุฑุจุทูˆุง ุญุงุฌุฉ ู‡ู†ุง ู„ูˆ ูƒุงู†ุช
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ู‡ุฐู‡ ุงุฑุชุจุทุช ู…ู† ููˆู‚ ู‡ุฐุง ุจุณู…ูŠู‡ tie ู„ูŠุดุŸ ู„ุฃู† ู‡ุฐุง ุจูŠู‚ุงูˆู…
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ู„ู„ุดุฏ ูˆู‡ุฐุง ุจูŠุจู‚ู‰ ุฅูŠุดุŸ ุจุงู„ู‚ูˆุงู… ุงู„ู„ูŠ ููŠ ุงู„ุฏุงุฎู„ุŒ ุฃูŠูˆุฉุŒ
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ู‡ุฐุง ุงู„ู€strap ุงู„ุขู† ู„ูˆ ุญุทูŠุช ุญุงุฌุฉ ุซุงู†ูŠุฉ ุฒูŠ ู‡ุฐู‡
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ูˆุญุทูŠุชู‡ุง ุนู„ู‰ ุงู„ู„ูŠ ุนู†ุฏูŠ ุชุญุชุŒ ุฅูŠุด ู‡ุ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„ุซุงู†ู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† ุฅูŠุดุŸ ูˆ ู‡ุงู† ุงู„ strut ูƒูƒู„
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ู‡ุฐุง ุนู„ู‰ ุจุนุถู‡ ุจู†ุณู…ูŠู‡ ุฅูŠุดุŸ ุ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 word ุงู„ุขู† ุฃู†ุง ุญุงุทุท ู„ู‡ุง ุฃุฌูˆุจุฉ
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ู…ุด ุญุงุทุท ู„ู‡ุง ุณูˆุงุก ุนู„ู‰ ุทูˆู„ ู‡ุฐุง ุงู„ู…ูุฑูˆุถ ุญุงุทุท ู„ู‡ุ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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ุฅูŠุดุŸ a reaction ุงู„ุขู† ุนู†ุฏูŠ statically determinate
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ุฅูŠุด ูŠู‚ูˆู„ู†ุง ุงู„ statically determinateุŸ ู†ุ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„ุขู† ุงู„ equilibrium ุฅูŠุด
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ุนู†ุฏูŠุŸ ุนู†ุฏูŠ load ุฃูˆ forces ูˆ ููŠ ุนู†ุฏูŠ counter force ุฃูˆ
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load ุนู†ุฏู‡ุง ู„ู…ุง ุฅุซู†ู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„ุขู† ุฅุทู„ุน ุนู†ุฏูŠ ู‡ู†ุง ุฅูŠุด ู…ูˆุฌูˆุฏ ุนู†ุฏูŠุŸ ู‡ูŠ ุงู„ trust
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ุงู„ู„ูŠ ู…ูˆุฌูˆุฏ ุนู†ุฏูŠ ู‡ู†ุง ุฅูŠุด ุนู†ุฏูŠุŸ forces ู„ูˆ ุญุทูŠุช ู…ุซู„ุงู‹
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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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ุฃู…ุงูƒู† ู…ุญู…ูˆู„ ุนู„ูŠู‡ู… satellite dish ูŠุนู†ูŠ ู‡ุงุฏ ุฌุงูŠ ุนู„ู‰
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ูˆูŠู†ุŸ ุนู„ู‰ ุงู„ุณุทุญ ุงู„ู„ูŠ ู‡ุงุฏ ุงู„ุขู† ู†ู‚ุทุฉ ุงู„ result sense
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ุชุจุนู‡ู… ูˆูŠู†ุŸ ู‡ุงุฏ ุชูƒูˆู† ู‡ุงุฏ ุงู„ุขู† ู‡ุ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„ุขู† 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 calculation In 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 single resultant ู…ุญุตู„ุฉ ู…ุธุจูˆุท ููŠ ุงู„
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diagram ุงุซู†ูŠู† ู‡ุฐู‡ ุตุงุฑุช ุชู„ุงุชุฉ ูˆุงุญุฏุฉ ูƒูŠู ุจุนู…ู„ู‡ู…ุŸ ุ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 ุฅูŠุด ุณู…ู†ุงู‡ู… ู‡ุฏูˆู„
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ุงู„ joints ู‡ุฏูˆู„ุฉ flexible ูˆู„ุง rigidุŸ flexible ู„ูˆ ุฃู†ุง
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ุถุบุท ุนู„ูŠู‡ู… ุจุชุญุฑูƒูˆุง ู…ุธุจูˆุท ูู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 ู‚ู„ู†ุงุŸ truss ู…ุธุจูˆุท ุงู„ุขู† ุงู„ู„ูŠ ู‚ู„ู†ุง ุงู„
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trust ุงู„ู„ูŠ ู‡ูˆ ุฅูŠุดุŸ ุนู†ุฏูŠ frame with flexible joint
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ุฃูˆ pin joint ู…ุด rigid ุงู„ู„ูŠ ุนู†ุฏูŠ ุฏูŠ ุฅูŠุดุŸ 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 red ุงู„ู„ูŠ ุฃู†ุชูˆ
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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„ุขู† 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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ุฅูŠุด ู‡ูŠุŸ ู‡ุฐูŠ Straight ู‡ุฏูŠ Straight ู‡ุฏูŠ Tie ู‡ุฏูˆู„
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ุงู„ุดุบู„ุงุช ุจุฏูƒูˆุง ุชุนุฑููˆู‡ุง ู„ุฃู† ู‡ุฏูŠ ู…ู† ุงู„ุดุบู„ุงุช ุงู„ุณู‡ู„ุฉ
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ุทูŠุจ choose the correct word from the bracket to
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complete the sentences ุจุฏู†ุง ุงู„ูƒู„ู…ุฉ ุงู„ุตุญู‰ traces
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are frameworks or ties ุฅูŠุด ุงู„ trace framework with
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ุฅูŠุด ูŠู‚ูˆู„ ู„ูˆ ุฏูŠ flexible ุฃูˆ joint ุฃูˆ pin jointsุŒ
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ู…ุธุจูˆุทุŸ ุทูŠุจ ุงู„ connection between members which
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flexes is calledุŸ pin joint ู…ุด rigidุŒ ูƒูˆูŠุณุŸ struts
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are designed to resist compression ูˆู„ุง tension?
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compression ุทู„ุน ุนู†ุฏ ุงู„ tie ุฅูŠุดุŸ ุงู„ tie ุงู„ู„ูŠ ู‡ูŠ
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ุนู…ู„ูŠุฉ ุงู„ ุฅูŠุดุŸ ุงู„ tensionุŒ ุฃูŠูˆุฉ ู‡ุฐู‡ ุนู…ู„ูŠุฉ ุงู„ tension
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ุ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 ูˆู„ุง being joined making
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it stiffer embraced embraced ุงู„ู„ูŠ ู‡ูŠ ุฅูŠุด ู‚ู„ู†ุง ุนู†ู‡ุง
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embraced ุงู„ู„ูŠ ู‡ูŠ ู„ู…ุง ู†ู‚ูˆู„ ุนู†ู‡ ุฅูŠุด ุจูŠุนู…ู„ู„ู†ุง stiffen
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00:22:33,790 --> 00:22:43,050
ูˆ brace ู†ูุณ ุงู„ุดูŠุก ู„ู…ุง ู†ุนู…ู„ ุงู„ stiffen ู‡ุงูŠ ุทูŠุจ ุงู„ุขู†
260
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ุฏู‡ ุจู†ุทู„ุน ุงุญู†ุง ุฅูŠุด ุงู„ู„ูŠ ู…ุฑ ุนู„ูŠู†ุง ุงู„ูƒู„ู…ุงุช ููŠ ู‡ู†ุง
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ุงุชูƒู„ู…ู†ุง ููŠ ุงู„ chapter ู‡ุงูŠ ุนู„ู‰ ุงู„ structural
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mechanics ุชูƒู„ู…ู†ุง ููŠู‡ ุนู„ู‰ .. ุฃูˆู„ุง ู‚ู„ู†ุง ู„ู…ุง ุงู„ frame
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ุ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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ุนู†ุฏูŠุŸ ุนู†ุฏูŠ two different forces ุฃูˆ two different
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loads of 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„ู‰
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ุญุงุฌุฉ ุชุงู†ูŠุฉ ุจุนุฏู‡ุง ู‡ุฐุง ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ุฌุฒุฆูŠุฉ ู‡ุฐู‡ ุงู„
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gravity ูˆ ุงู„ center of gravity ุงู„ gravity ู‡ูŠ ุฅุญุฏู‰
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ุงู„ forces ุจุชุฃุซุฑ ุนู„ู‰ ูƒู„ ุดูŠุก ูˆ ุฏุงุฆู…ุง ุงุญู†ุง ุจุชูƒูˆู†
272
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downward ูˆ ู…ู…ูƒู† ุฃู†ุชู… ุจุชุนุฑููˆู‡ุง ูƒูŠู ุชุญุณุจูˆู‡ุง ุงู„ู„ูŠ ู‡ูŠ
273
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ุจุชุณุงูˆูŠ M ููŠ G ู…ุธุจูˆุทุŸ ุฃู‚ูˆู„ ู„ูƒู… ููŠ ุงู„ููŠุฒูŠุงุก ู…ุฑุช
274
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
275
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ุงู„ gravity ูƒุฏู‡ ุจุชุณุงูˆูŠุŸ ุชุณุนุฉ point ุซู…ุงู†ูŠุฉ ูˆุงุญุฏ
276
00:24:04,180 --> 00:24:08,160
meter squared per second ู…ุธุจูˆุท ุฃูˆ meter per second
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00:24:08,160 --> 00:24:12,520
squared ุงู„ุขู† ุงู„ู„ูŠ ุนู†ุฏูŠ ู‡ุฐู‡ ุงู„ู„ูŠ ุจู†ุชุทู„ุน ุนู„ูŠู‡ุง ุงู„ุขู†
278
00:24:12,520 --> 00:24:18,520
ู„ู…ุง ู†ูŠุฌูŠ ุจุนุฏ ู‡ูŠูƒ ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ structure with
279
00:24:18,520 --> 00:24:22,280
different joint ู‚ู„ู†ุง ุงู„ joints ู„ู…ุง ุชูƒูˆู† flexible
280
00:24:22,280 --> 00:24:27,780
ุจู†ุณู…ูŠู‡ุง pin joint ูˆ ู„ู…ุง ุชุจู‚ู‰ hard ุฃูˆ solid ุจู†ุณู…ูŠู‡ุง
281
00:24:27,780 --> 00:24:33,000
ุฅูŠุด rigid joints ุงู„ุขู† ุงุชูƒู„ู…ู†ุง ุนู„ู‰ ุงู„ structure ุชุจุนู‡
282
00:24:33,000 --> 00:24:37,440
ุฏู‡ ุงู„ structure ุงู„ู…ูˆุฌูˆุฏ ุนู†ุฏูŠ with flexible ุฃูˆ ุจูŠู†
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00:24:37,440 --> 00:24:43,680
joint ุณู…ู†ุงู‡ traces ุฃูˆ trace ุงู„ุขู† ุงู„ู„ูŠ ุนู†ุฏูŠ ููŠ ุงู„
284
00:24:43,680 --> 00:24:48,940
trace ุนู†ุฏูŠ ููŠู‡ member ุฏู‡ ุงู„ member members resist
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00:24:48,940 --> 00:24:53,840
compression ุณู…ู†ุงู‡ู… ุฅูŠุดุŸ stress ูˆ ุฏู‡ ุนู…ู„ูˆุง
286
00:24:53,840 --> 00:25:00,670
resisting ู„ู„ tension ุณู…ู†ุงู‡ู… ุฅูŠุดุŸ tie ู‡ูƒุฐุง ุฎู„ุตู†ุง