--- title: "Screw jack with square thread" subject: "Machine Design II" chapter: 8 key: "semester_7/machine_design_ii:screw-jack-square-thread-numerical" source: https://www.bctengineer.com/q/semester_7/machine_design_ii/screw-jack-square-thread-numerical site: BCT Engineering --- # Screw jack with square thread Machine Design II · Chapter 8: Power screw - Asked in: year not given, 8 marks - Video: [Design Of Screw Jack Numerical 2 Part 2 - Design Against Static Loads - Machine Design I](https://www.youtube.com/watch?v=CAacgKzwx0Q) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/machine_design_ii/screw-jack-square-thread-numerical - Whole chapter: https://www.bctengineer.com/md/semester_7/machine_design_ii/chapter-8 ## Question A screw jack lifts a load of 25 kN. It has a single-start square thread of nominal diameter 50 mm and pitch 8 mm. The coefficient of friction on the thread is 0.12. The load rests on a collar of mean radius 32.5 mm with a friction coefficient of 0.15. Find (a) the torque to raise the load, (b) the torque to lower the load, (c) the overall efficiency, and whether the screw is self-locking, (d) the direct stress in the screw core and the torsional shear stress in it, and (e) the number of threads and height of a nut if the bearing pressure is limited to 8 MPa, and the shear stress in the nut thread. ## Short answer With helix angle 3.17° and friction angle 6.84°, raising torque is 223 N m, lowering 159 N m, overall efficiency 14.2%, screw is self-locking. Compressive stress 18 MPa, torsional shear 7 MPa. Nut needs 6 threads, height 48 mm. ## Answer #### Data $W = 25\,000$ N, $d = 50$ mm, $p = 8$ mm (single start, lead $L = 8$ mm), $\mu = 0.12$, $R_c = 32.5$ mm, $\mu_c = 0.15$. Mean diameter: $d_m = d - p/2 = 46$ mm. Core diameter: $d_c = d - p = 42$ mm. Helix angle: $\alpha = \tan^{-1}\dfrac{8}{\pi\times46} = 3.169^\circ$. Friction angle: $\varphi = \tan^{-1}0.12 = 6.843^\circ$. #### (a) Torque to raise $$ T_1 = W\tan(\alpha+\varphi)\frac{d_m}{2} = 25000\times\tan(10.012^\circ)\times0.023 = 101.5\ \text{N m} $$ Collar torque: $T_2 = \mu_c W R_c = 0.15\times25000\times0.0325 = 121.9$ N m. $$ T = T_1 + T_2 = 223.4\ \text{N m} $$ #### (b) Torque to lower $$ T_{l} = W\tan(\varphi-\alpha)\frac{d_m}{2} + T_2 = 25000\times\tan(3.674^\circ)\times0.023 + 121.9 = 36.9 + 121.9 = 158.8\ \text{N m} $$ #### (c) Efficiency and self-locking Efficiency of the screw alone: $\eta_s = \dfrac{\tan\alpha}{\tan(\alpha+\varphi)} = \dfrac{0.05536}{0.17657} = 31.4\%$. Overall efficiency including collar: $$ \eta = \frac{W L}{2\pi T} = \frac{25000\times0.008}{2\pi\times223.4} = 14.2\% $$ Since $\varphi = 6.84^\circ > \alpha = 3.17^\circ$, a positive torque is needed to lower the load: the screw is **self-locking**. #### (d) Stresses in the screw Direct compressive stress on core: $$ \sigma_c = \frac{4W}{\pi d_c^2} = \frac{4\times25000}{\pi\times42^2} = 18.0\ \text{MPa} $$ Torsional shear (thread torque $T_1$ acts on the screw core): $$ \tau = \frac{16T_1}{\pi d_c^3} = \frac{16\times101500}{\pi\times42^3} = 7.0\ \text{MPa} $$ Maximum shear $= \tfrac12\sqrt{18.0^2 + 4\times7.0^2} = 11.4$ MPa (small, safe). Buckling is checked as a column if the unsupported length is large. #### (e) Nut The bearing area of the threads is the projected annulus $\dfrac{\pi}{4}(d^2-d_c^2)$ per turn, so: $$ n = \frac{4W}{\pi(d^2-d_c^2)\,p_b} = \frac{4\times25000}{\pi(2500-1764)\times8} = 5.4 \;\Rightarrow\; n = 6 $$ Nut height $H = n\,p = 6\times8 = 48$ mm. Shear stress in nut thread (thickness $t = p/2 = 4$ mm): $$ \tau_n = \frac{W}{\pi d\,t\,n} = \frac{25000}{\pi\times50\times4\times6} = 6.6\ \text{MPa} $$ (the nut thread shears at the major diameter; the stress is low for a bronze nut.) **Answer:** $T_{raise} = 223$ N m; $T_{lower} = 159$ N m; $\eta = 14.2\%$ overall; self-locking; $\sigma_c = 18$ MPa, $\tau = 7$ MPa; nut with 6 threads, height 48 mm. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For d = 50 mm and p = 8 mm, the mean and core diameters are A. 46 mm and 42 mm B. 42 mm and 46 mm C. 50 mm and 42 mm D. 54 mm and 58 mm Answer: A. d_m = d - p/2 = 46 mm and d_c = d - p = 42 mm. (Key point: Mean and core diameters) 2. The total torque to raise the load is made of A. Thread torque only B. Thread torque plus collar friction torque: T = T_1 + mu_c W R_c C. Thread torque minus collar torque D. Collar torque only Answer: B. T_1 = 101.5 N m and T_2 = 121.9 N m give 223.4 N m. (Key point: Total raising torque) 3. Why is this screw self-locking? A. alpha = 3.17 degrees is greater than phi = 6.84 degrees B. phi = 6.84 degrees is greater than alpha = 3.17 degrees, so torque is needed to lower C. The overall efficiency is above 50% D. The collar friction is zero Answer: B. Since phi > alpha, tan(phi - alpha) is positive and effort is needed to lower the load. (Key point: Self-locking) 4. The number of threads is found from A. The shear stress in the screw core B. The bearing pressure on the projected thread area: n = 4W/(pi (d^2 - d_c^2) p_b) C. The torque on the collar D. The core diameter alone Answer: B. This gives n = 5.4, taken as 6, so nut height H = 6 x 8 = 48 mm. (Key point: Number of nut threads) ## Related in Machine Design II - [Torque and efficiency of a power screw](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Apower-screw-torque-efficiency-derive) — Machine Design II, chapter 8 - [Power screw threads, standards and materials](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Ascrew-thread-types-standards-stress) — Machine Design II, chapter 8 - [Maximum efficiency and ball screws](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aself-locking-maximum-efficiency-ball-screw) — Machine Design II, chapter 8 - [Helical spring under fluctuating load](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aspring-fatigue-soderberg-design) — Machine Design II, chapter 6 - [Simple band brake absorbing power](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aband-brake-power-absorbed) — Machine Design II, chapter 7 - [Gear ratios of a four-speed car](https://www.bctengineer.com/question.md?key=semester_7%2Fmachine_design_ii%3Aautomobile-gear-ratio-selection) — Machine Design II, chapter 5 ## Related in other subjects - [Thread errors and effect of pitch error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Ascrew-thread-errors-and-pitch-effect) — Metrology, chapter 12 - [Screw thread production and change gears](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Ascrew-thread-manufacturing-change-gears) — Manufacturing and Production Processes, chapter 11 - [Measuring thread pitch, angle and diameters](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Atoolmaker-microscope-thread-measurement) — Metrology, chapter 12 - [Friction pile length, 350 mm, 1200 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afriction-pile-350mm-1200kn) — Foundation Engineering, chapter 8