GATE — Agricultural Engineering (AG) · India · IITs and IISc on rotation (2026: IIT Guwahati)
Original practice questions written to the published syllabus · not past papersSizing the parts of farm machines so they do not fail: shafts, keys, joints, springs, bearings, drives and overload devices.
In the exams: GATE AG Section 2 Machine Design (belts, spur gears, shear pins recur); ICAR AICE subject 39 Units 1–2; NCEES PE machinery component design
GATE — Agricultural Engineering (AG)
Section 2 names machine design. Numerical and NAT items recur on belt drives (tension ratio, power, centrifugal tension, V-belt wedge), spur gear strength (Lewis, tangential force, module), shear pin diameter for a given breaking torque, chain drives and shaft sizing under combined bending and torsion. Expect one or two machine design calculations each year.
How our questions for GATE spread across the units of Machine Design. Difficulty: 19 easy, 43 medium, 26 hard.
| Belt and chain drives | 11 | |
| Stress concentration and fatigue (Goodman and Soderberg) | 9 | |
| Shafts under combined bending and torsion | 8 | |
| Spur gear design (Lewis and Buckingham) | 8 | |
| The design process, materials and factor of safety | 7 | |
| Rolling and sliding bearings and bearing life | 7 | |
| Bolted joints | 6 | |
| Springs | 6 | |
| Overload safety devices: shear bolts and slip clutches | 6 | |
| Measurement of force, torque and strain on machine elements | 6 | |
| Keys and couplings | 5 | |
| Knuckle and cotter joints | 5 | |
| Welded joints | 4 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
Steel with a tensile yield strength of 400 MPa is used for a part in pure shear. According to the distortion energy theory, what is its yield strength in shear?
D. 231 MPa
Distortion energy theory gives Ssy = Syt / sqrt(3) = 0.577 x 400 = 231 MPa. 200 MPa is the maximum shear stress theory value (0.5 Syt). 283 MPa is 400 / sqrt(2), which is not a failure theory result.
Further reading: Budynas & Nisbett, Shigley's Mechanical Engineering Design
A steel link has a stress amplitude of 100 MPa and a mean stress of 150 MPa. Its corrected endurance limit is 250 MPa, yield strength 400 MPa and ultimate strength 600 MPa. What is the factor of safety by the Goodman criterion?
C. 1.54
Goodman: 1/N = sigma a/Se + sigma m/Sut = 100/250 + 150/600 = 0.400 + 0.250 = 0.650, so N = 1.54. Soderberg uses Syt: 1/N = 0.400 + 0.375, N = 1.29. Gerber (parabola) gives 1.92. Se/sigma a = 2.50 ignores the mean stress.
Further reading: Budynas & Nisbett, Shigley's Mechanical Engineering Design
A steel link has a stress amplitude of 100 MPa and a mean stress of 150 MPa. Its corrected endurance limit is 250 MPa, yield strength 400 MPa and ultimate strength 600 MPa. What is the factor of safety by the Soderberg criterion?
D. 1.29
Soderberg: 1/N = sigma a/Se + sigma m/Syt = 100/250 + 150/400 = 0.400 + 0.375 = 0.775, so N = 1.29. Using Sut (Goodman) gives 1.54. Syt/(sigma a + sigma m) = 1.60 is only the first-cycle yield check. Multiplying the ratios instead of adding them is an algebra slip: 1/(0.400 x 0.375) = 6.67.
Further reading: Budynas & Nisbett, Shigley's Mechanical Engineering Design
A tractor PTO delivers 15 kW at 540 rpm to an implement. What torque does the PTO shaft carry?
A. 265 N m
T = 60 P / (2 pi n) = 60 x 15000 / (2 pi x 540) = 265 N m. Dividing power by rpm directly gives 27.8, and forgetting the factor 60 (treating n as rev/s) gives 4.42 N m. 531 N m drops the 2 from 2 pi n (60 x 15000/(pi x 540)).
Further reading: Bhandari, Design of Machine Elements
Why does a high preload improve the fatigue life of a bolt in a joint under fluctuating external load?
C. The stiff clamped members absorb most of the load fluctuation, so the alternating stress in the bolt is small
With preload, only the fraction C = kb/(kb + km) of the external load change reaches the bolt while the joint stays closed, so the bolt's stress amplitude is small even though its mean stress is high. Preload does not change material properties or thread geometry, and it does not change stiffnesses.
Further reading: Budynas & Nisbett, Shigley's Mechanical Engineering Design
A shaft of 60 mm diameter is welded to a plate by a circumferential fillet weld of 6 mm leg and carries a torque of 1 kN m. What is the shear stress in the weld throat?
A. 41.7 MPa
Throat t = 0.707 x 6 = 4.24 mm. For a thin ring of throat t at radius d/2, J = pi t d^3/4 and tau = T (d/2)/J = 2T/(pi t d^2) = 2 x 10^6/(pi x 4.24 x 60^2) = 41.7 MPa. Using the leg size gives 29.5 MPa; dropping the 2 in 2T/(pi t d^2) gives 20.8 MPa; 16T/(pi d^3) = 23.6 MPa is the stress in the solid shaft, not the weld.
Further reading: Bhandari, Design of Machine Elements
A roller chain of 15.875 mm pitch connects sprockets of 17 and 51 teeth at a centre distance of 635 mm. The centre distance can be adjusted slightly, and the chain length is to be rounded up as recommended for roller chains. What chain length, in links, should be used?
A. 116 links
Ln = 2C/p + (z1 + z2)/2 + ((z2 - z1)/(2 pi))^2 p/C = 80.0 + 34 + 0.73 = 114.73, rounded up to the next even number, 116, to avoid an offset link. Rounding up to 115 links, an odd number, would need an offset (cranked) link, which is weaker; forgetting to halve (z1 + z2) gives 148.73, rounded up to 150 links, and using C/p instead of 2C/p gives 74.73, rounded up to 76.
Further reading: Bhandari, Design of Machine Elements
A spur gear has 40 teeth and a pitch circle diameter of 160 mm. What is its module, and what is the usual textbook choice of face width?
D. 4 mm; about 40 mm
m = d/z = 160/40 = 4 mm. Face width is usually taken as about 10 m (range about 9.5 m to 12.5 m), so about 40 mm. 0.25 is z/d, the inverse.
Further reading: Bhandari, Design of Machine Elements
A single active strain gauge (quarter bridge) with gauge factor 2.0 is excited at 5 V. The part strains by 1000 microstrain. What is the approximate bridge output?
C. 2.5 mV
Quarter bridge: Vo = V GF epsilon/4 = 5 x 2.0 x 0.001/4 = 0.0025 V = 2.5 mV. A full bridge of four active gauges gives about 10 mV, a half bridge 5 mV. 1.25 mV omits the gauge factor.
Further reading: Doebelin, Measurement Systems
Four active strain gauges in a full Wheatstone bridge, each with gauge factor 2.0, measure a strain of 1000 microstrain (two gauges in tension, two in compression, arranged so their outputs add). The excitation is 5 V. What is the approximate output?
C. 10 mV
For a full bridge with four equal active arms of alternating sign, Vo = V GF epsilon = 5 x 2.0 x 0.001 = 10 mV, four times a quarter bridge (2.5 mV). 40 mV multiplies the full-bridge value by 4 again.
Further reading: Doebelin, Measurement Systems
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