steel beam forum

A uniform steel beam has a mass of 1350 kg. On it is resting half of an identical beam, as shown in Fig. 9-50.

Cuddlebear , Sunday, 15th of August 2010 05:41:48 PM

A uniform steel beam has a mass of 1350 kg. On it is resting half of an 
Cuddlebear
identical beam, as shown in Fig. 9-50. What is the vertical support force 
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at each end?

left end

right end

Here is a 
Joined: Saturday, 15th of May 2010, 15:42:04
picture of the problem so you can get a better perspective. 
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http://i297.photobucket.com/albums/mm230/kamikaze205/Problem.jpg
 
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Lady Grey , Monday, 16th of August 2010 01:10:13 AM

Find the center of mass of the two beams. Treat the load as if  
Lady Grey
it were acting there.  
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Joined: Friday, 11th of June 2010, 14:18:37
call x=0 at left end. x=L at right end  
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xbar1 = L/2, m1 = 1350kg  
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xbar2 = L/4, m2 = m1/2  
 
xbar = (xbar1*m1+xbar2*m2)/(m1+m2)  
 
xbar = (m1*L/2 + m1*L/8)/(m1+m1/2)  
 
Result for COM:  
xbar = 5/12*L  
 
Call left support (RL), right support (Rr)  
 
Add up moments about left support:  
Rr*L = xbar*(m1+m1/2)*g  
 
Solve for Rr:  
Rr = 3*xbar*m1*g/(2*L)  
 
Result for right end:  
Rr = 5/8*m1*g  
 
Add up forces to find left end reaction:  
Rr + RL = (m1+m1/2)*g  
Rr + RL = 3*m1*g/2  
RL = 3*m1*g/2 - Rr  
 
Substitute Rr:  
RL = 3*m1*g/2 - 5/8*m1*g  
 
Result:  
RL = 7/8*m1*g  
 
Left end reaction: RL = 7/8*m1*g  
Right end reaction: Rr = 5/8*m1*g  
 
As numbers (m1 = 1350kg; g:=9.8 N/kg):  
Left end reaction: RL = 11,576.25 Newtons  
Right end reaction: Rr = 8,268.75 Newtons  
 
 
 
 
 
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