Finding Yield Strength, E, and TS

[tre2k3]

Heres my given problem:
Gauge Length = 2 in.
Area = 0.5 in^2

The specimen yields under a load of 32,000 lb
The corresponding gauge length is 2.0083 (the 0.2 yield point)

Max load = 60,000 lb @ gage length = 2.60 in

I need to determine the yield strength, modulus of elasticity, and Tensile strength


This problem has no graph, and this books has no examples


I tried to answer it by having ys= 32,000 lb/ 0.5 in^2 (6.895x10^-3 Mpa / 1 lb/in^2) = 441.28 MPa

e= (2.0083 - 2)/2 =.00415

E = 441.28/.00415 = 106 x 10^3 MPa

TS = 60,000/0.5 in^2 (6.895x10^-3 Mpa / 1 lb/in^2) = 827.4 MPa

Im no too sure about my answers because I can't find where it states explicitly how to get the yield strength or what the it is in terms of a formula

 

[PhanthomJay]

Your problem is given in units of pounds and inches, which are quite valid units in the USA and one or 2 other countries, so there is no need to convert to MPa. Pounds per square inch (psi) will suffice nicely.
The problem seems to have some inconsistencies and missing data and the missing graph. You note the the gauge length at the 0.2 yield point (that is e=.002) corresponds to its yield stress at that point. But the gauge length of 2.0083 corresponds to a strain of 0.004 (as you noted), which is inconsistent with a yield stress definition of stress at 0.2%strain. Then there is the problem of definition of tensile strength; and to calculate E, you really need to know the proportional limit stress prior to yield(i.e, separation between the elastic and plastic state). Now if the problem were to be simplified to an approximate curve with a straight line stress strain curve in the elastic region, with a slope of E up to its yield point at e=.002, then a horizontal line beyond yield to a certain strain value, then with an increasingly sloped lineto the max tensile stress, then the gage length at max load is not necessary, and you have for the yield strengh, ys=P/A = 32000/0.5 = 64000psi, which you have correrctly calculated (before your conversion to the ''forbidden' pascals!). And for the E modulus, that'd be yield stress over yield strain =64000/.002 = 32,000,000 psi; and your tensile strength is the given max load of 60000 pounds (120,000psi max stress per your correct calc). But I'm just approximating...a graph and more data would help. (the material looks a lot like 60ksi yield steel).

 

[piercas]

Based on the given information, it appears that you have correctly calculated the yield strength (YS), modulus of elasticity (E), and tensile strength (TS) for the given material. However, it is always important to double check your calculations and ensure that they are accurate.

The yield strength is typically determined by finding the stress at which the material begins to deform plastically, or permanently. This can be done by plotting a stress-strain curve and identifying the point at which the curve deviates from the linear elastic region. In this case, the yield point is given as 0.2% strain, which is commonly used to define the yield strength.

The modulus of elasticity, also known as Young's modulus, is a measure of the stiffness of a material and is calculated by dividing the stress by the strain within the elastic region. It represents the slope of the linear portion of the stress-strain curve.

Finally, the tensile strength is the maximum stress that a material can withstand before it fails in tension. This is typically determined by performing a tensile test and measuring the maximum load at failure.

Overall, your approach to calculating these values seems reasonable based on the given information. However, it is always important to verify your results and consult additional resources or experts if you have any doubts or uncertainties.