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Shearing stress  timber truss 
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#1
Sep208, 10:34 PM

P: 35

1. The problem statement, all variables and given/known data
member AD of the timber truss shown (attached) is framed into the 100 X 50 mm bottom chord ABC as shown (attached  detailed view). determine the dimension 'a' that must be used if the average shearing stress parallel to the grain at the ends of the chord ABC is not to exceed 2.25 MPa 2. Relevant equations shearing stress, tau = V/A where V is shear force, A is cross sectional area > average 3. The attempt at a solution is my free body diagram correct? if so, do i first solve for the forces in each member using the method of joints. do i consider that the chord in question is also the same at where the roller is located? once i have found all the forces in each member based on the free body diagram do i just use what i found to be the force at C as the value for V in the shearing stress formula? do i then just solve for A aka 'a'? please tell me if i am on the right track, if not, any assistance appreciated 


#2
Sep308, 01:16 PM

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Your FBD is not correct. There can be no horizontal external A_x force at the pin A, because there are no other external forces in that direction to balance it. The reaction loads at supports A and C are both vertical only. Determine what they are, and solve for the tensile force in the bottom chord. The shear plane is not the cross section area of the lower chord, it is the plane parallel to the grain of length 'a' and 50mm in width. Your figure is a bit confusing, I think the chord is 100mm deep and 50mm into the page (a 100 X 50mm timber).



#3
Sep308, 03:10 PM

P: 35

when i solve for the tensile force in the bottom chord, is the best way to do this is:
 treat the bottom chord as the sum of the two 2m pieces is the average shearing stress a component of an angle, there is none given or am i meant to deduce the angle from finding out the reactions etc? 


#4
Sep308, 03:11 PM

P: 35

Shearing stress  timber truss
when i solve for the tensile force in the bottom chord, is the best way to do this is:
 treat the bottom chord as the sum of the two 2m pieces > find reactions/tensile in each 2m portion and then sum them is the average shearing stress a component of an angle, there is none given or am i meant to deduce the angle from finding out the reactions etc? 


#5
Sep308, 03:42 PM

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#6
Sep308, 09:22 PM

P: 35

after checking the solutions, the dimension for a should be 53.3mm, i am getting 80mm.
after doing the method of joints here are my values for the reactions F_BA = F_BC = 9kN F_BD = 18kN F_DA = F_DC = F_CD = 12kN Cy = Ay = 7.94kN see attachment for corrected free body diagram and angles calculated from given dimensions ultimately solving for a using tau = V/A 2.25MPa = 9kN/0.05a > a = 0.08m = 80mm 


#7
Sep408, 03:21 PM

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#8
Dec709, 10:17 AM

P: 1

from what book did you get this problem? thnx 


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