Strength of Materials Stress Question

[coolguy16]

Homework Statement

Member AD of the timber truss (shown in attachment) is framed into the 100 x 150 mm bottom chord ABC as shown in the insert. Determine the dimension "a" that must be used if the average shearing stress parallel to the grain at the ends of chord ABC is not to exceed 2.25 MPa.

Homework Equations

The Attempt at a Solution

T=V/A
I found the tension in AB to be 12 kN and the tension in AD to be -15 kN. I'm confused on how to find V and the cross section area? What would the thickness be of the the bottom chord according to this figure? Thanks.

 

[PhanthomJay]

Negative tension is compression. What is the horizontal force at the joint tending to shear (horizontally tear at the notch ) the bottom chord over the width a? What is the shear area you should use to calculate the shear stress ?

 

[coolguy16]

Hey thanks for replying. The horizontal force of the bottom chord would be equal to the tension of AB which would be 12kN. So summing the forces in the y-direction,
∑Fy = V = 12 kN. (I'm not sure if this value is correct.) I still do not understand the cross sectional area. The question states that the timber truss is framed into a 100 x 150 mm bottom chord but the diagram shows 100 mm and 50 mm. I'm not sure which number represents the width or depth. Can you please explain this part to me? Thanks.

 

[SteamKing]

Hey thanks for replying. The horizontal force of the bottom chord would be equal to the tension of AB which would be 12kN. So summing the forces in the y-direction,
∑Fy = V = 12 kN. (I'm not sure if this value is correct.) I still do not understand the cross sectional area. The question states that the timber truss is framed into a 100 x 150 mm bottom chord but the diagram shows 100 mm and 50 mm. I'm not sure which number represents the width or depth. Can you please explain this part to me? Thanks.

If you look at the detail of the joint carefully, you'll see that the total depth of the member is 100 mm + 50 mm = 150 mm from top to bottom.

Since the timber is specified as being 150 mm × 100 mm, this implies that the width of bottom chord is 100 mm.

 

[coolguy16]

So 100 x 150 -mm is referring to width x depth, thus the cross section would be a x width?

 

[PhanthomJay]

Yes.

 

[coolguy16]

Just to clarify, does the "a" represent the length from the timber truss parallel to the grain?

 

[PhanthomJay]

Just to clarify, does the "a" represent the length from the timber truss parallel to the grain?

The dimension a is as shown. Shear area is area in the same plane as shear force.

 

[coolguy16]

Alright thanks for the help.