Stress Calculation for a Reinforced Timber Tie with Aluminium Bar

[anthonyk2013]

Have to give this question ago for Monday, Wondering if I am on the right track.

A rectangular timber tie, 180mm by 80mm, is reinforced by a bar of aluminium of 25mm diameter. calculate the stress in the timber and reinforcement when the tie carries an axial load of 300KN
E of timber=15GN/m^2
E of aluminium=90GN/m^2

Area of timber=180*80=14400-3.14*25^2/4=13909mm^2

Area of aluminium=3.14*25^2/4=491mm^2

Next step is to find strain I think ε of timber=ε of aluminium

ε=δ/E so δ/E of timber=δ/E of aluminium, use this to find stress?

Could anyone teel me if I am on the right track?

 

[voko]

It is true that the strains must be equal. But stresses need not have to. The equation you ended up with contains two different stresses. While this might be what you had in mind, it is not obvious from what you wrote. So this is an equation with two unknowns. You need another equation, which can be obtained by considering that the timber and the bar must support the applied load.

 

[anthonyk2013]

It is true that the strains must be equal. But stresses need not have to. The equation you ended up with contains two different stresses. While this might be what you had in mind, it is not obvious from what you wrote. So this is an equation with two unknowns. You need another equation, which can be obtained by considering that the timber and the bar must support the applied load.

Yes I have two unknowns both stresses. I have E of both materials, not sure what equation I need next.

 

[Chestermiller]

Have to give this question ago for Monday, Wondering if I am on the right track.

A rectangular timber tie, 180mm by 80mm, is reinforced by a bar of aluminium of 25mm diameter. calculate the stress in the timber and reinforcement when the tie carries an axial load of 300KN
E of timber=15GN/m^2
E of aluminium=90GN/m^2

Area of timber=180*80=14400-3.14*25^2/4=13909mm^2

Area of aluminium=3.14*25^2/4=491mm^2

Next step is to find strain I think ε of timber=ε of aluminium

ε=δ/E so δ/E of timber=δ/E of aluminium, use this to find stress?

Could anyone teel me if I am on the right track?

ε=δ/E? This equation in incorrect. The strain is not equal to the displacement divided by E. The strain is equal to the stress divided by E. So use this to determine the stress in each of the two materials in terms of ε. From that you can get the force in terms of ε.

Chet

 

[anthonyk2013]

Sorry chester your 100% right. I mixed the displacement symbol and stress symbol up. That should read strain=stress/E

Sorry about that. Will correct as soon as I can get on my laptop.

 

[anthonyk2013]

I have corrected the stress symbols sorry if I confused anyone. any help would be appreciated.

Have to give this question ago for Monday, Wondering if I am on the right track.

A rectangular timber tie, 180mm by 80mm, is reinforced by a bar of aluminium of 25mm diameter. calculate the stress in the timber and reinforcement when the tie carries an axial load of 300KN
E of timber=15GN/m^2
E of aluminium=90GN/m^2

Area of timber=180*80=14400-3.14*25^2/4=13909mm^2

Area of aluminium=3.14*25^2/4=491mm^2

Next step is to find strain I think ε of timber=ε of aluminium

ε=σ/E so σ/E of timber=σ/E of aluminium, use this to find stress?

Could anyone teel me if I am on the right track?

 

[Chestermiller]

Yes. You're on the right track. Now determine the stresses in terms of ε and the forces in terms of ε. The total force is equal to the sum of the individual forces.

 

[anthonyk2013]

Yes. You're on the right track. Now determine the stresses in terms of ε and the forces in terms of ε. The total force is equal to the sum of the individual forces.

This is where I am puzzled. I need to determine the stress in term of ε, ε=ΔL/L I don't have ΔL/L so I need to find another way of finding ε from what I have been given?

Only one I can think of is ε1=-vε2 but don't have ant of the strains.

 

[Chestermiller]

This is where I am puzzled. I need to determine the stress in term of ε, ε=ΔL/L I don't have ΔL/L so I need to find another way of finding ε from what I have been given?

Only one I can think of is ε1=-vε2 but don't have ant of the strains.

You don't need to know L or ΔL. You are going to be solving for ε. That's your unknown.

 

[anthonyk2013]

You don't need to know L or ΔL. You are going to be solving for ε. That's your unknown.

Let 1 be aluminium
let 2 be timber

To solve for ε- σ1/E1=σ2/E2→σ1=σ2*E1/E2

σ1=σ2*90/15→σ1=σ2*6

σ1=σ2*6 use this to solve loads?

 

[Chestermiller]

Let 1 be aluminium
let 2 be timber

To solve for ε- σ1/E1=σ2/E2→σ1=σ2*E1/E2

σ1=σ2*90/15→σ1=σ2*6

σ1=σ2*6 use this to solve loads?

Sure. This is fine also. Try it both ways to see which appeals to you more.

 

[anthonyk2013]

Sure. This is fine also. Try it both ways to see which appeals to you more.

what would the other way be?

σ1=6*σ2

F=300KN

F=σ1*A1+σ2*A2

F=6*σ2*491+13909

F=(6*491*13909)σ2

F=16855σ2

300=16855σ2 → σ2=300/16855=.0177KN

σ2=.0177KN?M^2

σ1=6*.0177=106.8KN/M^2

 

[Chestermiller]

$$\sigma_1=E_1\epsilon$$
$$\sigma_2=E_2\epsilon$$
$$F=(E_1A_1+E_2A_2)\epsilon$$

 

[anthonyk2013]

$$\sigma_1=E_1\epsilon$$
$$\sigma_2=E_2\epsilon$$
$$F=(E_1A_1+E_2A_2)\epsilon$$

Thanks Chester, a quick question.
When solving these problems do I need to Create an equation depending on what values I have been given, where I'm having trouble is which one of the values to use first.
e.g. If I selected E of timber first I would have ended up with 15/90. Is there a selection process or will it all work out to the same answers.

 

[Chestermiller]

Thanks Chester, a quick question.
When solving these problems do I need to Create an equation depending on what values I have been given, where I'm having trouble is which one of the values to use first.
e.g. If I selected E of timber first I would have ended up with 15/90. Is there a selection process or will it all work out to the same answers.

The method I indicated doesn't give preference to either. Try doing the problem by selecting E for the aluminum first, and see what you get. You should find that you get the same answer. So it doesn't really matter.

 

[anthonyk2013]

Thanks again.

 

[anthonyk2013]

is 0.0177*10⁹ the same as 17.7MN/m²