A hole 3cm in diameter is to be punched out of a steel plate 8cm thick. The shear stress of the material is 670GPa. What load is required on the punch?
3cm = 0.03m
8cm = 0.08m
Lateral surface area
(As) = pi*D*h
= 3.1416 * .03m * .08m
= 3.1416 * .0024m
= .007539m
Force = Stress * Area
= 670GPa * .007539m
= 5.05113GN
= 5051.13MN
The load required is 5051.1MN.
Is this correct? Thank you.
Shearing stress (tangential stress)
τ=V/A,
where V ia resultant shearing force which passes through the area A being sheared.
V= τA=τ•πdh
Shear force is equal to the punching force P
P=τπdh=
=670•10⁹•3.14•0.03•0.08 =
=5.05•10⁹Pa =5.05GPa
That is correct.
perimeter of circle x thickness
(pi x d) x 0.08m
pi x 0.03 m x 0.08 m = 0.0075396 m2
stress = load / area
load = stress x area = 670 GPa x 0.0075396 m2
= 670 GN/m2 x 0.0075396 m2
= 5.051532 GN or 5051.532 MN
Well, well, well, looks like someone's punching holes through steel plates! That's quite a feat! Let me crunch some numbers and see if you got it right.
Let's see, you calculated the lateral surface area correctly, which is impressive. But when it comes to the force calculation, I have a little surprise for you. The equation you used is correct, but you forgot to convert the shear stress from gigapascals (GPa) to pascals (Pa).
So, let's fix that little mishap. The shear stress needs to be multiplied by 1 billion to convert it from GPa to Pa. Let's try it again, shall we?
Stress = 670 GPa * 1 billion Pa/GPa
= 670,000,000,000 Pa
Now, we can calculate the force correctly.
Force = Stress * Area
= 670,000,000,000 Pa * 0.007539 m
= 5,048,930,000 N
= 5.04893 MN
Ta-da! The load required on the punch is approximately 5.04893 MN. So close, but not quite there. Keep those calculations going, and you'll be a steel-punching pro in no time!
Yes, your calculation is correct. The load required on the punch is 5051.13 MN.
Yes, your calculations are correct. The load required on the punch is indeed 5051.1MN (meganewtons). To arrive at this result, you correctly calculated the lateral surface area (As) of the hole using the formula pi * D * h, where D is the diameter of the hole (in meters) and h is the thickness of the steel plate (also in meters). You then multiplied the shear stress of the material (670 GPa) by the lateral surface area (As) to obtain the force required.
It is worth noting that the shear stress is usually given in units of pascals (Pa), not gigapascals (GPa). So, to get the shear stress in pascals, you would need to divide 670 GPa by 10^9. However, since you used the same unit (GPa) to calculate the force, your final answer is still correct in meganewtons (MN).