# Shearing stress - timber truss

• portofino
In summary: After doing the method of joints, you should have the following values for the reactions:F_BA = F_BC = 9kNF_BD = 18kNF_DA = F_DC = F_CD = 12kNCy = Ay = -7.94kN
portofino

## Homework Statement

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

## Homework Equations

shearing stress, tau = V/A where V is shear force, A is cross sectional area --> average

## 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

#### Attachments

• fbdtruss.JPG
13.6 KB · Views: 1,073
• detailed.JPG
16 KB · Views: 736
• fbdtt.JPG
12.5 KB · Views: 740
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).

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?

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?

portofino said:
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
No, whether they are 2 pieces or one piece does not matter. They do not add. The tension in AB is the same as the tension in BC. If you isolate joint B, you should see that in the x direction, the tension in AB must be equal to the tension in BC (AB tension points left, BC tension points right). But first, in order to arrive at that tension value, you should determine the vertical reactions and then isolate joint A and solve for the member forces at that joint using the method of joints. Have you determined the vertical reactions? Are you familiar with the method of joints? Note it is given that member AD has a slope of 1.5/2.
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?
This problem is a bit tricky, in that usually in a pure truss one deals with axial tension or compression forces only. In this case, you have a tensile force in AB due to the horizontal component of AD, that is pushing the member AB outward (to the left). That introduces a longitudinal shear in the wood timber over the length 'a' and 50mm width, trying to split and tear the wood apart in shear across that plane. To calculate the distance 'a', note that the shear stress is equal to the tensile force in AB divided by the shear plane area, that is parallel to the load, of (.050)(a).

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

#### Attachments

• angle.JPG
15.3 KB · Views: 586
portofino said:
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

portofino said:

## Homework Statement

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

## Homework Equations

shearing stress, tau = V/A where V is shear force, A is cross sectional area --> average

## 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

this exact problem was given to us as an assignment.
from what book did you get this problem? thnx

## What is shearing stress in a timber truss?

Shearing stress in a timber truss refers to the force that is applied parallel to the cross-sectional area of the truss, causing it to deform or fail.

## How does shearing stress affect the stability of a timber truss?

Shearing stress can cause the individual members of a timber truss to slide past each other, reducing the overall stability and load-bearing capacity of the truss.

## What factors can contribute to shearing stress in a timber truss?

There are several factors that can contribute to shearing stress in a timber truss, including the weight of the load, the span of the truss, and the type of joinery used.

## How can shearing stress be prevented in a timber truss?

To prevent shearing stress in a timber truss, it is important to design the truss with adequate bracing and support, use high-quality materials, and ensure proper installation and maintenance.

## What is the difference between shear stress and bending stress in a timber truss?

Shear stress refers to the force applied parallel to the cross-sectional area of the truss, while bending stress refers to the force applied perpendicular to the cross-sectional area. Both types of stress can affect the stability and strength of a timber truss.

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