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Hibbeler Statics 11th Ed. Problem 9-22

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rooya

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Date Posted: 7/20/2008 7:34:45 AM Status: Live

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Response:

figure 1------parabola

figure 2------triangle

we know that Mass m=ρtA

ρ=mass density

t=thickness

A=Area of the plane

For parabola

considering the vertical strip

dA=ydx

dA=√2x dx

intigrating from 0 to 2

=2.67

A1=2.67m^2

we know that

x1=3.2/A= 3.2/2.67 =1.198m

simillarly y1=0.75m

For triangle

x2=1.33m

y2= -0.67m

A2=2 m^2

m1=ρtA1

m2=ρtA2

centroid for the composit figure

Xc= (m1*x1+m2*x2)/(m1+m2)

Xc=(A1*x1+A2*x2)/(A1+A2) (since ρt term cancles in the numerator and denominator)

Xc=1.25m

simillarly

Yc=0.14m

Reactions at A and B

taking momenta about A

Rb*2√2=W*1.25

Rb*2√2=(m1+m2)g*1.25

Rb*2√2=ρt(A1+A2)g*1.25

Rb*2√2=7850*0.3(2.67+2)*9.81*1.25

Rb=47687.81N

using ΣFx=0 and ΣFy=0 u can get Rx and Ry

if u still find any difficulty please specify

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Hibbeler Statics 11th Ed. Problem 9-22

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