# Elongation of a bar problem | Timoshenko

• Engineering
• newbie1127
In summary, the author has a problem with calculating the change in length of a steel bar and a wooden beam. He used the equation E = 30 x 10^6 lb/sq.in and A = 1 sq.in, but the answer came out to be 0.005 inch different than the author's answer of 0.060 inch.
newbie1127
Homework Statement
Determine the cross-sectional dimensions of the wooden beam BC and of the steel bar AB of the structure ABC, loaded at B, if the workin stress for pine wood is taken as crw = 160 lb per sq in. and for steel a~ = 10,000 lb per sq in. The load P = 6,000 lb. The dimensions of the structure are shown in Fig. 7. Determine the vertical and the horizontal components of the displacement of the point B due to deformation of the bars. Neglect the weight of the structure.
Relevant Equations
d(Change in length) = (Load x Length) / (E x Area)
hi everyone,

In a problem where we have to find the change in length of a steel bar and a wooden beam,
while calculating the change in length the author multiplied the entire thing by 12

I put all the values in the above equation and still couldn't account for the 12.

Thinking of it nothing more than a print mistake i moved on, only later to find the same thing in the same type of problem.
I'll put all the values down below to paint a more detailed picture:

Length of bar = 15 inch
Tension on bar = 10000 lb
E = 30 x 10^6 lb/sq.in
A = 1 sq.in

After putting all these in the equation, the answer comes out to be 0.005 inch. However, the author has answer as 0.060 inch, differeing by a magnitude of 12x

I don't know why it is like that. help please

some reference :

the figure and solution offered by author - I'll attach a screenshot of these

#### Attachments

• Screenshot from 2022-04-15 10-31-22.png
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Where does the problem come from?
Maybe the original bar length was 15 feet, but has now been changed to 15 inches, and the answer did not have the 12 inches per foot conversion removed.

newbie1127
Baluncore said:
Where does the problem come from?
Maybe the original bar length was 15 feet, but has now been changed to 15 inches, and the answer did not have the 12 inches per foot conversion removed.
you're right Mr.baluncore, it is the problem, thanks :)

Baluncore
I see your problem on page 11. You are not the first to read it that way.
Now you know the advantage of using the MKSA international system of units.

Baluncore said:
I see your problem on page 11. You are not the first to read it that way.
Now you know the advantage of using the MKSA international system of units.
thanks for not roasting me.
i also prefer the SI system, but i could only find this book in the inch system.

## 1. What is the Timoshenko method for calculating elongation of a bar?

The Timoshenko method is a mathematical approach used to calculate the elongation of a bar under applied loads. It takes into account both shear deformation and bending deformation, making it more accurate than traditional methods which only consider bending deformation.

## 2. How is the Timoshenko method different from other methods?

The Timoshenko method differs from other methods in that it takes into account the effect of shear deformation on the elongation of a bar. This is important for bars with high aspect ratios or when the material has low shear modulus.

## 3. What are the assumptions made in the Timoshenko method?

The Timoshenko method assumes that the bar is homogeneous, isotropic, and linearly elastic. It also assumes that the cross-sectional area of the bar remains constant and that the material properties are constant along the length of the bar.

## 4. How is the Timoshenko method applied in real-world engineering problems?

The Timoshenko method is commonly used in structural engineering to calculate the deflection and stress of beams and other structural elements. It is also used in the design of mechanical components such as shafts and axles.

## 5. Are there any limitations to the Timoshenko method?

While the Timoshenko method is more accurate than traditional methods, it still has limitations. It may not be suitable for highly non-uniform or non-homogeneous materials. It also does not take into account other factors such as temperature and creep, which may affect the elongation of a bar in real-world applications.

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