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<br />
<br />(R+ l/tJ SII"
<br />
<br />Assum. CuI 01 crown
<br />
<br />I ,s oss/lm~d cons(onl
<br />
<br />,
<br />
<br />..,
<br />)
<br />
<br />UNIFORM CIRCULAR SECTION
<br />
<br />COEFFICIENTS FOR MOMENTS, SHEARS AND THRUSTS
<br />
<br /> (1) (1)
<br />, Sl. ~ Cos ~ M' "
<br />,
<br />O' 0 1.000 0 +.2500
<br />15 .259 .966 -.0335 +.2165
<br />30 .SOO ,866 -.1250 +.1250
<br />'5 .707 .707 -.2500 0
<br />'" .866 .500 -:3750 -.1250
<br />75 .966 .259 -.4665 -.2165
<br />90 1.000 0 -.5000 -.2500
<br />(1) Coefficients of wR (R + t)
<br />(2) Coefficients of w (R + t)
<br />
<br />(1)
<br />
<br />(1)
<br />M !F
<br />,
<br />
<br />,
<br />(2), (2)
<br />:Fh
<br />
<br />iN
<br />
<br />In
<br />
<br />"h
<br />
<br />-.0833 +.1667: 0 I .333
<br />t-----l..----
<br />-.0722 +.l443_+:_2~~3~_~~_:.:~8
<br />-.0417 +.0833 i .500 i .289 i .289 i .500
<br />! . _ _"_-'--~ ----t____
<br />I ' J I '
<br />o ----l---~_L.707. .236 .33~~~
<br />+.0417 -.0833"~ .167 .2894-.833
<br />+.0722 -.1443 I .966 .086 .167 I .955
<br />+.0833 ' -.1667 1.000 0 0 --tl~o~
<br />
<br />o
<br />
<br />,
<br />-,-
<br />
<br />
<br />(2)
<br />
<br />.333
<br />
<br />EM 1110-Z-2902, Appendix III. 3 Mar 1969
<br />
<br />For one quadrant:
<br />
<br />ds
<br />
<br />((/2 41'CR + t/Z)
<br />(R + t/2)d~ :Eds" (R + t/2l.{' d~ .. 2
<br />-.. s'a~ IR' ti LIR' '151'~ ~]
<br />w. 51n2 ~2(R + tl R (statica1l1lOl1lentl
<br />
<br />M'
<br />
<br />..
<br />
<br /> ,",
<br />I M'ds .R (R + 'I {R + tlZl.,{' sln2, dflll
<br /> .R (R + ,) (R + tlZl <f .<fR IR + t) (R + '/1)
<br /> 1 '," 8
<br />
<br />.<fR
<br />M. IM'ds
<br />1"'~'"
<br />
<br />(R + t) (R + t/Z)
<br />8
<br />.-f (R + tl2)
<br />1
<br />
<br /> .R {R+t} (indeterminate ITfJment)
<br /> d
<br />M M. ... .. (R+tl . s1n29' (R+ t) R
<br /> , , . . 1
<br />M .. (R' t) sinZ,
<br /> , .
<br />
<br />M
<br />,
<br />
<br />cos Z fill
<br />wR(R+t}~
<br />
<br />Moment at any point dul" to vertical load only
<br />
<br />Mh
<br />
<br />1/3 Mv
<br />
<br />Moment due to horizontal load only
<br />
<br />M
<br />
<br />Moment due to horizontal and vertical loads
<br />
<br />: M + M
<br />, h
<br />
<br />Fv w(R + t) sin fill Vertical component of total T04d on any section
<br />
<br />Fh j (R + t) cos fill Horizontal component of total load on any section
<br />
<br />v
<br />
<br />F v cos fill - Fh sin fill Total shear on any section
<br />
<br />N F v sin, + Fh cos fill Total normal load (thrust) on any section
<br />
<br />,
<br />
<br />This table is based on the assumption that the horizor.',,-,. "'Jrth
<br />
<br />o'
<br />
<br />pressure will be one-third of the vertical. For a submerged condition,
<br />
<br />15
<br />
<br />use natural drained wei9hts above the groundlooater surf..c,' ',,'J ~'"'.H ",_
<br />welghts belQ\O and apply the coefficients in the tabll". 'oJ.,'"' I,.r. .._,] i
<br />
<br />30
<br />
<br />.5
<br />60
<br />7S
<br />90
<br />
<br />uniform hydrostatic pressure is assumed for the water ~,e 'c,,, .t,~ ,i:!"("JtlV'
<br />
<br />line, and adjusted coefficients for Mh and Fh should ~,e ce".,.uted ~s "hre..
<br />times the values in the table. v and N, for the watt:r ::,;::',<,ure, should then
<br />
<br />be comouted by the formulas.
<br />
<br />ANALYSIS (f UNIFORM CIRCUL~ SECTlIIt
<br />
<br />111-15
<br />
<br />PLATE
<br />
<br />7
<br />
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