Konular

6.4 A Cylindrica Specimen of a Titantum Alloy Having an Elastic Modulus of 107 GPa (15.5times 10^6psi) and an Original Diameter of 3.8

Soru

6.4 A cylindrica specimen of a titantum alloy having an elastic modulus of 107 GPa (15.5times 10^6psi) and an original diameter of 3.8 mm (0.15 in.)will experience only elastic deformation when a tensile load of 2000 N (450 Iby) is applied.Compute the maximum length of the specimen before deformation if the maximum allowable clongation is 0.42 min (0.0165 in).

Çözüm

4.6 (323 Oylar)

Deniz

Uzman doğrulaması

Elit · 8 yıl öğretmeni

Cevap

To solve this problem, we need to use the formula for elastic deformation:

where:-

is the strain (deformation),-

is the stress,-

is the elastic modulus.Given:- Elastic modulus,

- Original diameter,

- Tensile load,

- Maximum allowable elongation,

First, we need to calculate the original cross-sectional area

of the specimen:

Substituting

:

Next, we calculate the maximum allowable stress

:

Substituting

and

:

Now, we can find the maximum allowable strain

:

Substituting

and

:

Finally, we can find the maximum length

before deformation:

Solving for

:

Substituting

and

:

Therefore, the maximum length of the specimen before deformation is approximately 256.10 mm.