Spring Load
Made from a 0.25 inch diameter wire, a helical torsion spring has a mean spring diameter of 5 inches. If the spring’s bending stress is 5,000 lb/in^2 due to a load applied 2.5 inches away from the coil’s center, what is the applied load in lb?
Expand Hint
For a helical torsion spring, the bending stress is:
$$$\sigma=K_i(\frac{32Fr}{\pi d^3})$$$
where
$$K_i$$
is the correction factor,
$$F$$
is the applied load,
$$r$$
is the radius from the coil’s center to the load, and
$$d$$
is the wire diameter.
Hint 2
Correction factor:
$$$K_i=\frac{(4C^2-C-1)}{[4C(C-1)]}$$$
where
$$C=D/d$$
,
$$D$$
is the mean spring diameter, and
$$d$$
is the wire diameter.
Correction factor:
$$$K_i=\frac{(4C^2-C-1)}{[4C(C-1)]}$$$
where
$$C=D/d$$
,
$$D$$
is the mean spring diameter, and
$$d$$
is the wire diameter.
First, let’s solve for
$$C$$
:
$$$C=\frac{5in}{0.25in}=20$$$
Next, solve for the correction factor:
$$$K_i=\frac{(4(20)^2-(20)-1)}{[4(20)(20-1)]}=\frac{(1,600-20-1)}{[80(19)]}=\frac{1,579}{1,520}=1.0388$$$
For a helical torsion spring, the bending stress is:
$$$\sigma=K_i(\frac{32Fr}{\pi d^3})$$$
where
$$K_i$$
is the correction factor,
$$F$$
is the applied load,
$$r$$
is the radius from the coil’s center to the load, and
$$d$$
is the wire diameter.
$$$5,000\frac{lb}{in^2}=1.0388\times \frac{32F(2.5in)}{\pi (0.25in)^3}$$$
$$$F=62.5\frac{lb}{in^3}\times \frac{\pi (0.25in)^3}{1.0388}=2.95\:lb$$$
2.95 lb
Time Analysis
See how quickly you looked at the hint, solution, and answer. This is important for making sure you will finish the FE Exam in time.- Hint: Not clicked
- Solution: Not clicked
- Answer: Not clicked
Similar Problems from FE Sub Section: Springs
135. Helical Spring
141. Tensile Strength for Springs
205. Compression Spring
206. Spring Force
265. Mechanical Springs
335. Spring Stretch
339. Compressing a Spring
341. Parallel Springs
343. Springs in Series
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
478. Spring Stretching
484. Correction Factor
486. Bending Stress
575. ASTM 232
576. Applied Force
Similar Problems from FE Section: 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
485. Mean Stress
486. Bending Stress
516. Power Screw Torque
520. Power Screw Load
540. Bearing
547. Power Screw Lead
565. Design Life
575. ASTM 232
576. Applied Force
577. Preload
589. Threaded Load
590. Minimum Tensile
591. Joint Coefficient
594. Threaded Preload
596. Tensile Area
603. Bearing Type
630. Type of Bearing