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419_Mechanics Homework Mechanics of Materials Solution

# 419_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: *4.157 as“! 4.158 The couple M acts in a vertical plane and is applied to a beam of the cross section shown. Determine the stress at point A. PROBLEM 4.158 SOLUTION 40mm Dsihﬂ Mo'hr‘s (2(th o'e‘l'ermfne. 'Hae Pn'ncfpaﬂ 10mm lies and +LQ Fn‘ncx‘Pa/p Momen+5 0‘? \‘ner'f‘l'm. M=1.2kN. T -i:l L , CAI-J 10 mm 70 mmvl |~10 mm I9 = 1.894 X 106 mm4 1, = 0.614 x 106 mm“ 1?; = +0300 x 106 mm4 Yf I.8‘i‘fjo.3oo) >410“ mm 2 (0.51%, 0.20cbjxlo‘ MI»: E (1.9254J o )xlo" m‘ q R: “‘FH F2“ = o,cqo‘+o.soo‘>«lo’ - :.o2q5xzo"m. -6 Iv: (1.2sq—I-oz~+5)xlo‘m* = 0-227910”; Mm”: 0-2295'x/o w." -6 L, : (1.254 + i.02~+5')><lo° M“ ? 2.272920" W." : 2.27asx/o w." — .5; _ M = 9 = 2537* +am 29.. - FE * 0.8‘io-nlo‘ l.25 m MV = M cos 9M = (l.2><103)6qs 25.67" = [ADSHQMO3 MM Mu : _ Msln 9“ = —(I.2x[0“’)sim 25.47" = -O£148r!o" N-m Us "' 3’» cos 9“ - 24 5:» 9.. =- Lks‘cus. 25167°«-'45‘ an 25.0": 2L0"? m V3 "-' a cos 9.“ + NA sin 9.... '-' 45 Cos 25.6704- 45- .sn'n 252\$?) ? £0.05 MM -3 - _ 3 60.0 no") 5A 2 __ Mv u, + Mﬂv, :_([email protected])§2i.o7xgo )+ (05193“0 X 5' Iv I” 0.12?5'x10" 2. 2785340“ : Hs.ox:o“Pa. : ”3.0 MPG, ...
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