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710_Mechanics Homework Mechanics of Materials Solution

# 710_Mechanics Homework Mechanics of Materials Solution -...

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Unformatted text preview: {ﬁm [ll—”lill—jl—l 771*} {I 3 PROBLEM 6.53 6.53 The design of a beam calls for connecting two vertical rectangular '3' x 4-in. plates by welding them to two horizontal %‘ x 2-in. plates as shown. For a vertical shear V, determine the dimension a for wlﬁch the shear flow through the welded surfaces is maximum. SOLUTION I = (zxrgxgwr + mama—)3 + mama:- = mower! + 203' in" Q= (NC-Ho. = a : 1,-9- '-"-————-—-—--—-———-V0' 3 J = O 3' I H.o'+leev+2o.‘ 3+ 3:. J (”.04 me: + 29)) - (coon) _ Hg” 1. V ‘ 0 a. 01.04:“? + 103-) 24.1 = 9.01““? 0- " LHZQ in. PROBLEM 6.54 7 6.54 (:3) Determine the shearing stress at point P of a thin-walled pipe of the cross 0 section uhowa caused by I. vertical shear V. (b) Show that the maximum shearing stress oectm for 9- 90° and is equal to 2V/A. whereA is the mutational area ofthe p1pe. SOLUTION A = “at Jr And . unit I-i-J'ewjt For an. area!“- m A,' 2ret Q," A} “ 2rts:n6 ’E = \_/_Q_P , V3 ”33"“6) . Van-l3 P (“3 1cm mt 1t) ‘ 1rV‘..‘t - in: V ““7“ 9T1?" 27* ...
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