## Mean Stress

With a joint coefficient of 0.3 and a preload of 5 lb, a threaded fastener is put under fatigue loading via an external force of 20 lb. Calculate the mean stress (psi) if the tensile-stress area is 0.5 in^2.

##
__
__**Expand Hint**

**Expand Hint**

Mean stress:

$$$\sigma_m=\sigma_a+\frac{F_i}{A_t}$$$

where
$$\sigma_a$$
is the alternating stress,
$$F_i$$
is the preload, and
$$A_t$$
is the tensile-stress area.

##
__
__**Hint 2**

**Hint 2**

If an externally applied load varies between zero and
$$P$$
, the alternating stress is:

$$$\sigma_a=\frac{CP}{2A_t}$$$

where
$$C$$
is the joint coefficient,
$$P$$
is the externally applied load, and
$$A_t$$
is the tensile-stress area.

Fatigue loading is the observed material changes under stress due to cyclic loading (which produces a range of stress levels). The mean stress is the arithmetic mean of both the max and min stresses. The alternating stress is the difference between the peak stresses and the mean stress.

If an externally applied load varies between zero and
$$P$$
, the alternating stress is:

$$$\sigma_a=\frac{CP}{2A_t}$$$

where
$$C$$
is the joint coefficient,
$$P$$
is the externally applied load, and
$$A_t$$
is the tensile-stress area.

$$$\sigma_a=\frac{(0.3)(20lb)}{2(0.5in^2)}=6\:psi$$$

Mean stress:

$$$\sigma_m=\sigma_a+\frac{F_i}{A_t}$$$

where
$$\sigma_a$$
is the alternating stress,
$$F_i$$
is the preload, and
$$A_t$$
is the tensile-stress area.

$$$\sigma_m=6psi+\frac{5lb}{0.5in^2}=6psi+10psi=16\:psi$$$

16 psi

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**Joining Methods**280. Joint Shear Stress

347. Bolt Diameter

458. Rivet Strength

480. Threaded Fastener Load

481. Max Tension Load

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**Mechanical Design and Analysis**135. Helical Spring

141. Tensile Strength for Springs

205. Compression Spring

206. Spring Force

265. Mechanical Springs

280. Joint Shear Stress

295. Planetary Gear

296. Roller Bearing

299. Ball Bearing

335. Spring Stretch

337. Power Screw

339. Compressing a Spring

341. Parallel Springs

343. Springs in Series

347. Bolt Diameter

371. Spring Compression

381. Series of Springs

384. Springs in Parallel

386. Compounding Springs

387. Spring Tensile Strength

388. Torsional Stress

392. Chrome Silicon Wire

456. Free Length Spring

458. Rivet Strength

478. Spring Stretching

480. Threaded Fastener Load

481. Max Tension Load

483. Fatigue Loading

484. Correction Factor

486. Bending Stress

516. Power Screw Torque

520. Power Screw Load