NCEES Prac Exam Question 537 MD&M

Does anyone understand the solution to this problem?

The solution ignores the given pitch value and calculates the thread lead based on the thread angle and mean diameter. 

Based on my understanding (and Shigley's), the thread lead should be equal to 3x the pitch because it is a triple-start thread. If you solve the power screw equations using lead equal to 5.25 in (3 x 1.75) you do not obtain the correct answer. My gut feeling is that the pitch value given in the problem of 1.75 inches is an error.

Any help would be appreciated.

I agree that there is definitely a mistake somewhere. From Shigley's Standard Handbook of Machine Design

Lead = Pitch X Number of Thread Starts (Eq. 1)

Tangent(Lead Angle) = Lead / (PI X Mean Diameter) (Eq. 2)

If you solve (Eq. 2) for the lead you get

Lead = Tangent(Lead Angle) X PI X Mean Diameter

So (Eq. 1) gives

Lead = 1.75 X 3 = 5.25 in

and (Eq. 2) gives

Lead = Tangent(3.033) X PI X 1.50 in = 0.250 in

Obviously not the same when they should be.

Some things that jump out at me as being weird. A thread pitch is usually never larger than a thread diameter in real practice. Usually it is around 1/4 to 1/6 the thread diameter.

The other thing is that the solution calculates the lead using (Eq. 2) and then triples it which makes no sense. If you have multiple thread starts the lead angle goes up.

I have been messaging NCEES on facebook about all these errors and they have told me they have forwarded my concerns to their manager of publications. I asked when an updated eratta would be available and they told me last week they plan to post updated eratta tomorrow. Hopefully all our questions will be answered tomorrow.