Structural Analysis

[BrownFox]

Please help me understand how the author came up with the formula for his analysis. He made it very simple and i don't know how he solved this. I tried to check one of the forces in O2 and O1 and they are correct. Thanks!

 

[DaveAtkins]

Looks like he used the method of joints.

DaveAtkins

 

[msquared48]

Kind of an offshoot of the Graphical Maxwell Diagram.

Mike McCann, PE, SE (WA)

 

[BAretired]

The author used the method of sections. The bracketed expression is the moment about the panel point 2m away from the support (point A); 0.75 is the normal distance d from A to the top chord. The force in the top chord is M/d.

In the case of O1, consider a vertical section cut through the top chord between F1 and F2. The moment about A is 2(Av-F1). The slope is tan^-1(2.42/6) = 21.97^o. The normal distance d=2sinθ = 0.748 which the author rounded to 0.75. The force O1 is M/d = 2(Av-F1)/0.75 as he shows.

In the case of O2, consider a vertical section through point A cutting the top chord. The moment about A is the bracketed expression. The normal distance is unchanged, leading to the expression shown by the author.

BA

 

[rb1957]

not sure why he's using the terms he is. for me O1 = -(Av-F1)/sin(22) ... not obvious why he'd have -2(Av-F1)/(2*sin(22)) ?

for me -D1*cos(17.5) = F2*cos(22) ? D1 = -F2*0.97 close to -1.5/1.54*F2 ?

another day in paradise, or is paradise one day closer ?

 

[BAretired]

rb1957,
Your answers are the same as his. You are using the method of joints whereas the author is using the method of sections.



BA

 

[rb1957]

i notice that some of the factors seem to be member lengths ? i was wonderng how his equations were being assembled ? maybe i'll look up "method of sections" ...

another day in paradise, or is paradise one day closer ?

 

[BrownFox]

Baretired,

you're right, he's using method of sections.

however, i find i hard to solve O3, D3, D4, D5 & D6 using method of sections. I used method of joints for these members.

can you also explain how he gOt D6 = D7 - D5 ?

Thanks!

 

[BAretired]

I find it hard to read the numbers on the sketch but I agree that for this truss configuration, the method of sections does not work well where the section passes through more than three members (i.e. O3, D3, D4, D5 and D6).

I could not find a calculation of O3 by the author, but he appears to be using the method of joints for D5 and D6. The stress diagram for the joint between D6 and D7 is shown on the second page, explaining why D6 = D7 - D5. It is a graphical representation of the method of joints.

For D3, he is using the method of sections but has to include the effect of D4 in his calculation. By inspection, D3 and D6 should be numerically equal but of opposite sign; the author found D3 = -7.3kN and D6 = 7.25kN.

BA

 

[rb1957]

i was looking into D6 = D7-D5 ... from a math perspective it looks odd, but i looked at the force vector diagram ... 4-5-6 is an isoscelles triangle, so vector sum (D4+D5) = D5 !

another day in paradise, or is paradise one day closer ?

 

[rb1957]

there are a lot of round-offs. if the dimensions are true (why not ?) then the angles are rounded off, and then the calc rounds again "0.61" is really 2.42/4 = 0.605.

another day in paradise, or is paradise one day closer ?