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notist
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I've been trying to solve a structural mechanics problem from the book Mechanics of Materials, but the results I acquired weren't very satisfying.
Here it is
[PLAIN]http://img42.imageshack.us/img42/4375/p17n.jpg
Average Stress: [tex]\sigma[/tex]= F/A
Torque: [tex]\vec{M}[/tex]=[tex]\vec{r}[/tex] x [tex]\vec{F}[/tex]
Equations of static
First of all, I defined a load applied at point B and direction DB, resulting from the application of equation of the average stress:
|[tex]\vec{F(B)}[/tex]|=40 KN and [tex]\vec{F(B)}[/tex]= -18.82 ex - 35.29 ey.
Now, let the reactions at points C and D be called Cx/Cy and Dx/Dy respectively, I first assumed the values of Dx and Dy were symetrical to those in F(B), so as to obey the equations of static.
From here I simply calculated the sum of every torque regarding to point C, in order to eliminate Cx and Cy. The equation is as follows
-18.82*0.45 + 0.135P+35.29*0.24=0, resulting in P=0, which is obviously false.
From here I thought I was mistaken about the values of Dx and Dy and decided to treat them as variables. Writing the equations of static, I got
Cx+Dx=18.82
Cy+Dy=P+35.29
And from the total Torque relative to point C,
-18.82*0.45 + 0.135*P+0.24*Dy=0
Obviously, the system is indeterminate, but it's impossible to get more linearly independente equations of static for the system, so I decided to analyse the free body diagram of the two bars separately.
For the bar BD, I calculated the total moment relative do point B, resulting in the equation
-0.45*Dx+0.24*Dy=0
For the bar AC, I calculated the total moment relative to point A:
-0.135*Cx+0.570*Cy=0
The system is now solvable, but it the result is still incorrect. My main question is, if there is any flaw in my logic, where is it? Acording to the solutions, the result is 62.7KN.
Here it is
Homework Statement
[PLAIN]http://img42.imageshack.us/img42/4375/p17n.jpg
Homework Equations
Average Stress: [tex]\sigma[/tex]= F/A
Torque: [tex]\vec{M}[/tex]=[tex]\vec{r}[/tex] x [tex]\vec{F}[/tex]
Equations of static
The Attempt at a Solution
First of all, I defined a load applied at point B and direction DB, resulting from the application of equation of the average stress:
|[tex]\vec{F(B)}[/tex]|=40 KN and [tex]\vec{F(B)}[/tex]= -18.82 ex - 35.29 ey.
Now, let the reactions at points C and D be called Cx/Cy and Dx/Dy respectively, I first assumed the values of Dx and Dy were symetrical to those in F(B), so as to obey the equations of static.
From here I simply calculated the sum of every torque regarding to point C, in order to eliminate Cx and Cy. The equation is as follows
-18.82*0.45 + 0.135P+35.29*0.24=0, resulting in P=0, which is obviously false.
From here I thought I was mistaken about the values of Dx and Dy and decided to treat them as variables. Writing the equations of static, I got
Cx+Dx=18.82
Cy+Dy=P+35.29
And from the total Torque relative to point C,
-18.82*0.45 + 0.135*P+0.24*Dy=0
Obviously, the system is indeterminate, but it's impossible to get more linearly independente equations of static for the system, so I decided to analyse the free body diagram of the two bars separately.
For the bar BD, I calculated the total moment relative do point B, resulting in the equation
-0.45*Dx+0.24*Dy=0
For the bar AC, I calculated the total moment relative to point A:
-0.135*Cx+0.570*Cy=0
The system is now solvable, but it the result is still incorrect. My main question is, if there is any flaw in my logic, where is it? Acording to the solutions, the result is 62.7KN.
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