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33g [email protected] Hgﬁmgg Mam 5M?w~z$ gafm?’§gmm, gamw 3%wa g??? L; gig? 4%: Wﬂj 6mm ﬁﬁigﬁ Problem 2.440 A rigid bar of weight W = 800 N hangs from three equally spaced vertical wires, two of steel and one of aluminum (see ﬁgme). The wires also support a load P aeting at the midpoint of the bar. The
diameter of the steel wires is 2 mm, and the diameter of the aluminum wire is 4 mm.
What load Pallow can be supported if the allowable stress in the steel wires is 220 MPa and in the aluminum wire is 80 MPa? (Assume 7E5 = 210 GPa and Ea = 70 GPa.) Rigid bar
of weight W Problem 2.440 A rigid bar of weight W = 800 N hangs from three
equally spaced vertical wires, two of steel and one of aluminum (see ﬁgure).
The wires also support a load P acting at the midpoint of the bar. The
diameter of the steel wires is 2 mm, and the diameter of the aluminum wire is4 mm. What load Pallow E5 = 210 GPa and ElI = 70 GPa.) can be supported if the allowable stress in the
steel wires is 220 MP3 and in the aluminum Wire is 80 MP3? (Assume SECTION 2.4 Statically Indeterminate Structures 97 STEEL WIRES 5=2mm (TS ALUMINUM WIRES A=4mm EA : 70 GPa = 220 MPa (7A = 80 MPa E5 = 210 GPa FREEBODY DIAGRAM 0F RIGID BAR F5 is Fs lP+W EQUATION 0F EQUILIBRIUM EFVBI’I : 0 2F5+FA~P~W=0 EQUATION 0F COMPATIBILITY FORCE DISPLACEMENT RELATIONS 8 S 5 25A _ FSL EA 5 A _ FAL
EAAA (Eq 1) (Eq 2) (Eqs. 3, 4) Rigid bar
of weight W
SOLUTION 0F EQUATIONS
Substitute (3) and (4) into Eq. (2):
F51. _ FAL (Eq 5)
ESAS EAAA '
Solve simultaneously Eqs. (1) and (5):
AA
F = P + ——’1—~—~—) . 6
A ( W)(EAAA + 255A: (Eq )
F ~ (P + W)( :A’ ) (Eq 7)
‘ EAAA + 2ESAS '
STRESSES IN THE WIRES
F A (P + W)EA
=  = ————————— E . 8
“A AA EAAA + 253A: ( q )
F, _ (P + W)E,
‘7‘ '" A: ' EAAA + 2155As (Eq' 9)
ALLOWABLE LOADS (FROM ﬁgs. (8) AND (9))
0A
PA = jig(EAAA + 2E,A5) — W (Eq. 10)
A
0.5
P: : E(EAAA + ZEsAs)  W (Eq. ll) SUBSTITUTE NUMERICAL VALUES INTO EQS. (10) AND (11): As = E: (2 mm)2 = 3.1416 mm2 AA = 3T— (4 mm)2 —= 12.5664 mm2 4
PA = 1713N
PS = 1504N Steel governs. Palm 2 1500 N 4—— ...
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This note was uploaded on 02/01/2008 for the course CEE 212 taught by Professor Lynch during the Winter '06 term at University of Michigan.
 Winter '06
 Lynch

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