How to Solve Mechanics Problems Involving Framed Structures

[PhanthomJay]

Ok let's crank it out. P1 is (20)(2.15) = 43 and P2 is (20/2)(2.15) = 21.5, so the vert load is 64.5 N. The moment about the support is 43[(2.15/2) +.1 + 4 sin15] + 21.5[(2.15/3) + .1 + 4 sin15] = 134.9 N-m. Or, if you look at the moment at the support in the free body of the slanted member, it's 64.5(4)(sin15) + 68.1 = 134.9 N-m...checks out OK.

 

[D44]

Using the bending equations, I have a value of approx 88Pa for the induced stresses.

Am I right in using the the biggest moment in the equation, which is at the ground?

 

[D44]

Sorry, 44.24MPa

 

[PhanthomJay]

Sorry, 44.24MPa

It's somewhere around there, I didn't calc out the numbers, but yes, max bending stress is Mc/I where M is the max moment (139 Nm) occurring at the support, which controls the overall frame structural design. The I term comes from the properties of the hollow circle, and c is its outside radius.

 

[M3_CSL]

Hi, i am having the same trouble with this assignment, mainly drawing the free body diagram of each section. Not sure exactly whether to draw it as a full frame or two separate parts.
thanks

 

[PhanthomJay]

Hi, i am having the same trouble with this assignment, mainly drawing the free body diagram of each section. Not sure exactly whether to draw it as a full frame or two separate parts.
thanks

First draw it as a full frame to determine reactions at the fixed support at the base. Then break it up into the horizontal piece and slanted piece separately to determine forces and moments in each of those members.

 

[M3_CSL]

Thanks, so for the horizontal piece, when your working out the vertical forces, how do you know whether to use the 20Mn or the 40Mn? and does it only have 2 downward forces due to the billboard and one moment force due to the slanted piece?
Thank you

 

[M3_CSL]

sorry i ment 20Nm and 40Nm

 

[PhanthomJay]

Thanks, so for the horizontal piece, when your working out the vertical forces, how do you know whether to use the 20 N/m or 40 N/m [/color]? and does it only have 2 downward forces due to the billboard and one moment force due to the slanted piece?
Thank you

The vertical load is the area of the distributed loading diagram. It's a combimation of a rectangle 20 x 2.15 and a triangle with a long leg of 2.15 and a short leg of 20. Total = 64.5 N. The moment at the right hand side of the horizontal member is the equal and opposite of the moment about that point from the given applied loadings.