Please keep at least one language enabled. || కనీసం ఒక భాషను ఎంచుకోండి.
Question 1
ప్రశ్న 1
A centrifugal pump foundation is subjected to the machine's permanent weight and a periodic unbalanced force during operation. Why is an ordinary static bearing-capacity check alone insufficient for assessing its performance?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A machine foundation must support permanent loads and withstand forces generated during machine operation. These dynamic forces can produce repeated displacement and acceleration of the foundation-soil system. The resulting movement depends on the forcing frequency, natural frequency, stiffness, mass and damping. A foundation may satisfy static bearing resistance while still experiencing unacceptable vibration. Dynamic performance, settlement, structural resistance and effects on adjacent equipment must therefore be considered together.
వివరణ:
Question 2
ప్రశ్న 2
Which statement correctly distinguishes the principal dynamic actions associated with rotating, reciprocating and impact-type machinery?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Rotating machinery can produce periodic excitation when mass is not perfectly balanced about the rotation axis. Reciprocating machinery develops inertia forces associated with the acceleration and deceleration of moving components. Impact-type machines introduce rapidly applied forces and may excite transient foundation vibrations. Their forcing characteristics influence the selection of a suitable foundation arrangement. The analysis should use relevant machine operating data instead of treating every machine as an identical source of excitation.
వివరణ:
Question 3
ప్రశ్న 3
A compact reciprocating compressor requires a comparatively massive and rigid foundation near ground level, while a large turbo-generator requires elevated equipment support and access beneath the machinery. Which preliminary foundation selection is most appropriate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A block foundation provides a comparatively massive and rigid support for suitable machinery. Its inertia and interaction with the supporting soil influence its dynamic response. A frame foundation can provide elevated equipment support and the space required for operation and maintenance. Large turbo-generators are examples where an appropriately designed frame arrangement may be suitable. Final selection depends on machine characteristics, vibration criteria, structural geometry and foundation-soil properties.
వివరణ:
Question 4
ప్రశ్న 4
A rigid machine-foundation block undergoes vertical displacement, horizontal displacement and rocking under dynamic loading. Which statement correctly interprets these movements?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A rigid foundation block can undergo translational and rotational movements. Vertical and horizontal translations describe displacement of the block in different directions. Rocking refers to angular movement about a horizontal axis. The mass distribution and soil resistance influence the frequencies and amplitudes associated with these movements. Although simplified calculations may examine one mode at a time, coupled response can be important in practical machine foundations.
వివరణ:
Question 5
ప్రశ్న 5
A machine-foundation system is displaced from equilibrium and released without any continuing periodic external force. In another situation, the same system is subjected to a continuously acting sinusoidal machine force. Which classification is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Free vibration occurs when a disturbed system moves under its own restoring and inertia effects without continuing external excitation. The motion is characterized by the system's natural frequencies and damping. Forced vibration occurs when an external time-varying action continues to excite the system. Rotating and reciprocating machines can produce periodic forcing during operation. The distinction is essential because a forced response depends on both machine excitation and the dynamic characteristics of the foundation-soil system.
వివరణ:
Question 6
ప్రశ్న 6
A pump shaft rotates at 1500 revolutions per minute. If the dominant unbalance force completes ONE excitation cycle per shaft revolution, what is the forcing frequency in hertz?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Frequency in hertz represents the number of cycles per second. The shaft speed is specified as 1500 revolutions per minute. Dividing by 60 converts this to 25 revolutions per second. Because the question specifies one excitation cycle per revolution, the forcing frequency is 25 Hz. A machine producing several excitation cycles per revolution would require a corresponding adjustment.
వివరణ:
Question 7
ప్రశ్న 7
A reciprocating machine operates at 900 revolutions per minute and generates TWO similar dynamic force cycles during every revolution. What is the corresponding excitation frequency of this specified force component?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The machine rotational speed is 900/60 = 15 revolutions per second. The specified excitation repeats twice during each revolution. Therefore the excitation frequency is 2(15) = 30 Hz. This is different from the fundamental rotational frequency of 15 Hz. Machine-foundation analysis should consider the relevant excitation harmonics rather than assuming that every force component acts once per revolution.
వివరణ:
Question 8
ప్రశ్న 8
An idealized machine-foundation system is represented by a single-degree-of-freedom undamped mass-spring model. If the effective vibrating mass is m = 2000 kg and the equivalent linear stiffness is k = 800000 N/m, what is the natural circular frequency? Use omega_n = sqrt(k/m).
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The natural circular frequency of the specified idealized system is omega_n = sqrt(k/m). The equivalent stiffness is 800000 N/m and the effective mass is 2000 kg. Their ratio is 800000/2000 = 400 s^-2. Taking the square root gives omega_n = 20 rad/s. The result applies to the assumed single-degree-of-freedom mode and should not be treated as every natural frequency of a real foundation.
వివరణ:
Question 9
ప్రశ్న 9
For a simplified vertical machine-foundation vibration model, the effective mass is 1000 kg and equivalent vertical stiffness is 400000 N/m. Using fn = [1/(2 pi)]sqrt(k/m) and pi = 3.1416, what is the natural frequency approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The natural circular frequency is obtained by dividing the stiffness by the effective mass and taking the square root. Here k/m = 400000/1000 = 400 s^-2. Therefore omega_n = sqrt(400) = 20 rad/s. The ordinary frequency is fn = 20/(2 pi) = approximately 3.18 Hz. Radians per second and hertz are different frequency units and should not be interchanged.
వివరణ:
Question 10
ప్రశ్న 10
A machine-foundation system undergoes periodic free vibration at a frequency of 5 Hz. What is its corresponding vibration period?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The vibration period represents the time required to complete one cycle. Frequency represents the number of cycles completed in one second. The two quantities are related by T = 1/f. For f = 5 Hz, the period is T = 1/5 = 0.20 s. This reciprocal relationship applies to periodic motion regardless of the particular machine-foundation application.
వివరణ:
Question 11
ప్రశ్న 11
A machine foundation has an undamped natural frequency of 12 Hz. A rotating machine mounted on it produces one dominant excitation cycle per revolution and operates at 720 revolutions per minute. Which condition is indicated by the idealized frequency comparison?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The operating speed corresponds to 720/60 = 12 revolutions per second. With one excitation cycle per revolution, the forcing frequency is therefore 12 Hz. The foundation's natural frequency is also specified as 12 Hz. Their ratio is unity, representing the classical resonance condition in the idealized oscillator model. A damped system has a finite response, but operation near this frequency can still cause excessive vibration.
వివరణ:
Question 12
ప్రశ్న 12
Which statement best describes damping in a vibrating machine-foundation-soil system?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Damping reduces vibration energy through mechanisms associated with the material and surrounding medium. Soil hysteresis and other internal processes can contribute material damping. Energy carried away from a foundation through propagating waves contributes radiation damping. These mechanisms influence the amplitude and decay of vibration. Their effects must be considered together with mass, stiffness and forcing frequency rather than assuming damping alone guarantees acceptable movement.
వివరణ:
Question 13
ప్రశ్న 13
For a single-degree-of-freedom mass-spring-damper system, take m = 1000 kg, k = 9000 N/m and viscous damping coefficient c = 1200 N s/m. Using critical damping ccr = 2sqrt(km) and damping ratio zeta = c/ccr, what are ccr and zeta?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Critical damping for the specified idealized system is ccr = 2sqrt(km). The product km is 9000(1000) = 9000000 in consistent SI units. Its square root is 3000, giving ccr = 6000 N s/m. The damping ratio is therefore zeta = 1200/6000 = 0.20. Because the ratio is below unity, the idealized system is underdamped.
వివరణ:
Question 14
ప్రశ్న 14
An underdamped single-degree-of-freedom system has undamped natural frequency fn = 10 Hz and damping ratio zeta = 0.60. Using fd = fn sqrt(1 - zeta^2), what is its damped natural frequency?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The damped natural frequency of the specified viscously damped oscillator is fd = fn sqrt(1 - zeta^2). The square of the damping ratio is 0.60^2 = 0.36. The square-root factor is therefore sqrt(1 - 0.36) = sqrt(0.64) = 0.80. Multiplying by 10 Hz gives fd = 8 Hz. This equation describes the free-vibration frequency of the underdamped single-degree-of-freedom system.
వివరణ:
Question 15
ప్రశ్న 15
A harmonically forced single-degree-of-freedom system has viscous damping ratio zeta = 0.10. At forcing-frequency ratio r = 1, use the displacement dynamic magnification factor M = 1/sqrt[(1 - r^2)^2 + (2zeta r)^2]. What is M?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The frequency ratio r = 1 corresponds to forcing at the undamped natural frequency. The term 1 - r^2 therefore becomes zero. The dynamic magnification expression reduces to M = 1/(2zeta) at this ratio. With zeta = 0.10, M = 1/0.20 = 5.00. The result is finite because viscous damping is included in the specified response model.
వివరణ:
Question 16
ప్రశ్న 16
An idealized machine foundation is subjected to harmonic force amplitude F0 = 2000 N and has stiffness k = 2.0 x 10^6 N/m. The forcing-frequency ratio is r = 1 and damping ratio is zeta = 0.20. Using static displacement amplitude Xst = F0/k and dynamic magnification M = 1/(2zeta) at r = 1, what is the steady-state displacement amplitude?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The equivalent static displacement amplitude is Xst = F0/k. Substitution gives 2000/(2.0 x 10^6) = 0.001 m, or 1.0 mm. At r = 1 and zeta = 0.20, the magnification factor is M = 1/0.40 = 2.5. Therefore the steady-state displacement amplitude is 2.5(1.0) = 2.5 mm. This is a simplified single-degree-of-freedom result and not a universal permissible vibration amplitude.
వివరణ:
Question 17
ప్రశ్న 17
A machine normally operates at a forcing frequency of 30 Hz, while its foundation-soil system has a natural frequency of 12 Hz. During startup, the machine speed increases continuously from zero to its operating speed. Which engineering assessment is most appropriate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The machine's forcing frequency increases as its operating speed rises. It can pass through the foundation's natural frequency of 12 Hz before reaching 30 Hz. The passage may excite a temporary resonant response. The resulting amplitude depends on damping, how rapidly the speed changes and other dynamic characteristics. Foundation design should consider relevant startup and shutdown conditions in addition to normal steady operation.
వివరణ:
Question 18
ప్రశ్న 18
An UNDAMPED single-degree-of-freedom machine-foundation system is subjected to a harmonic force whose frequency is twice the undamped natural frequency. Using M = 1/|1 - r^2| for r = 2, what is the steady-state displacement magnification factor?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The forcing-frequency ratio is r = 2. For the specified undamped model away from resonance, the magnification factor is M = 1/|1 - r^2|. The denominator is |1 - 4| = 3. Therefore M = 1/3, or approximately 0.333. The result shows that forcing above natural frequency can produce a displacement amplitude smaller than the corresponding static displacement amplitude.
వివరణ:
Question 19
ప్రశ్న 19
For a harmonically forced machine mounted on a linear spring and viscous damper, the FORCE transmissibility is defined as transmitted-force amplitude divided by disturbing-force amplitude. Under the conventional single-degree-of-freedom isolation model, which condition gives force transmissibility below unity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Force transmissibility describes the fraction of a harmonic disturbing force transmitted through the mounting system. In the conventional linear spring-damper model, transmissibility depends on frequency ratio and damping. The mathematical isolation region begins when r exceeds sqrt(2). Below this threshold, the transmitted force amplitude can equal or exceed the disturbing-force amplitude. Actual installation performance also depends on isolator stiffness, damping, machine speed and the suitability of the supporting structure.
వివరణ:
Question 20
ప్రశ్న 20
An ideal UNDAMPED vibration-isolation mounting has forcing-frequency ratio r = 3. For this exercise, the force transmissibility is T = 1/|1 - r^2|. What are the transmissibility and percentage reduction in transmitted-force amplitude relative to the disturbing-force amplitude?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The specified frequency ratio is r = 3. Substitution into the undamped transmissibility expression gives T = 1/|1 - 9| = 1/8. Therefore the transmitted-force amplitude is 0.125 times the disturbing-force amplitude. The corresponding percentage reduction is (1 - 0.125)100 = 87.5%. This estimate applies only to the stated idealized isolation model and assumes steady harmonic excitation.
వివరణ:
Question 21
ప్రశ్న 21
A machine-foundation system has equivalent stiffness k and effective vibrating mass m. If the effective mass becomes FOUR times its original value while stiffness remains unchanged, what happens to its undamped natural frequency under fn = [1/(2 pi)]sqrt(k/m)?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Natural frequency in the specified model is proportional to the square root of stiffness divided by mass. Here the stiffness remains unchanged. Increasing mass to four times its initial value changes the frequency by a factor of 1/sqrt(4). Therefore the new natural frequency is one-half of the original value. Increasing foundation mass may help change frequency separation, but adequate soil bearing and settlement performance must also be maintained.
వివరణ:
Question 22
ప్రశ్న 22
A vibration-sensitive control room is located beside a pumping station. The pump is supported on a separate machine-foundation block, and the discharge piping crosses between the two structural systems. Which detailing strategy is most appropriate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Machine vibration can be transmitted to nearby structures through the ground and through direct structural connections. Separating the machine foundation from adjacent slabs may help reduce direct transmission. Flexible or otherwise suitable pipe connections can accommodate relevant differential movement and vibration. Isolation joints must be detailed so that unintended rigid bridges are not created during construction. Equipment alignment, piping loads and the required vibration limits should also be considered.
వివరణ:
Question 23
ప్రశ్న 23
A rotating component has an equivalent unbalanced mass me = 5 kg at eccentricity e = 0.01 m from the rotation axis. Its angular speed is omega = 20 rad/s. Using the idealized rotating-unbalance force amplitude F0 = me e omega^2, what is F0?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Rotating mass unbalance can generate a periodic force whose amplitude depends on the unbalance mass, eccentricity and angular speed. The stated expression is F0 = me e omega^2. The angular-speed term is 20^2 = 400 s^-2. Substitution gives F0 = 5(0.01)(400) = 20 N. The quadratic dependence on angular speed explains why increasing rotational speed can substantially increase the unbalance force.
వివరణ:
Question 24
ప్రశ్న 24
For a simplified small-strain soil-dynamics model, the shear modulus is estimated by Gmax = rho Vs^2, where rho is soil mass density and Vs is shear-wave velocity. If rho = 1800 kg/m3 and Vs = 200 m/s, what is Gmax?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Shear-wave velocity is related to the stiffness of a soil mass under small-strain conditions. The given equation is Gmax = rho Vs^2. The squared wave velocity is 200^2 = 40000 m2/s2. Multiplying by the mass density gives Gmax = 1800(40000) = 72000000 Pa. Therefore the small-strain shear modulus is 72 MPa, although an appropriate strain-dependent stiffness may be required for practical foundation-response analysis.
వివరణ:
Question 25
ప్రశ్న 25
Which mapping correctly identifies the subjects of the revised IS 2974 machine-foundation provisions in the Indian Standards series?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The revised IS 2974 series provides Indian design and construction guidance for machine foundations. IS 2974 Part 1:2026 addresses general provisions. Part 2:2026 deals with block foundations, while Part 3:2026 addresses frame foundations. Part 4:2026 covers foundations for hammers and presses. This updated organization should not be confused with the titles of the older parts that were superseded.
వివరణ:
Answer Key సమాధానాల పట్టిక
-
Question 1 ప్రశ్న 1Answer: B. The machine-foundation-soil system can vibrate, so frequency, amplitude, damping and transmission of dynamic forces must also be evaluated. సమాధానం: B.
-
Question 2 ప్రశ్న 2Answer: D. Rotating unbalance can generate periodic forces, reciprocating components produce inertia forces, and impact machinery introduces short-duration dynamic actions. సమాధానం: D.
-
Question 3 ప్రశ్న 3Answer: A. Consider a rigid block foundation for the compressor and a suitably designed frame foundation for the turbo-generator. సమాధానం: A.
-
Question 4 ప్రశ్న 4Answer: C. Translation and rotation represent different possible vibration modes, and their interaction may be important in foundation response. సమాధానం: C.
-
Question 5 ప్రశ్న 5Answer: B. The first is free vibration, while the second is forced vibration. సమాధానం: B.
-
Question 6 ప్రశ్న 6Answer: A. 25 Hz. సమాధానం: A.
-
Question 7 ప్రశ్న 7Answer: D. 30 Hz. సమాధానం: D.
-
Question 8 ప్రశ్న 8Answer: C. 20 rad/s. సమాధానం: C.
-
Question 9 ప్రశ్న 9Answer: A. 3.18 Hz. సమాధానం: A.
-
Question 10 ప్రశ్న 10Answer: B. 0.20 s. సమాధానం: B.
-
Question 11 ప్రశ్న 11Answer: D. The forcing frequency is 12 Hz and coincides with the natural frequency, indicating the classical resonance condition. సమాధానం: D.
-
Question 12 ప్రశ్న 12Answer: C. Damping represents mechanisms that dissipate or carry away vibrational energy, including material and radiation damping, and influences vibration amplitude. సమాధానం: C.
-
Question 13 ప్రశ్న 13Answer: A. 6000 N s/m and 0.20. సమాధానం: A.
-
Question 14 ప్రశ్న 14Answer: B. 8 Hz. సమాధానం: B.
-
Question 15 ప్రశ్న 15Answer: D. 5.00. సమాధానం: D.
-
Question 16 ప్రశ్న 16Answer: A. 2.5 mm. సమాధానం: A.
-
Question 17 ప్రశ్న 17Answer: C. The machine may pass through a resonant frequency during startup, so transient response, damping and the time spent near resonance should be considered. సమాధానం: C.
-
Question 18 ప్రశ్న 18Answer: B. 0.333. సమాధానం: B.
-
Question 19 ప్రశ్న 19Answer: D. Frequency ratio r greater than sqrt(2), subject to the stated idealized model. సమాధానం: D.
-
Question 20 ప్రశ్న 20Answer: C. T = 0.125; reduction = 87.5%. సమాధానం: C.
-
Question 21 ప్రశ్న 21Answer: A. It becomes one-half of the original frequency. సమాధానం: A.
-
Question 22 ప్రశ్న 22Answer: B. Provide appropriate foundation isolation joints and flexible or properly designed pipe connections to limit unwanted vibration transmission and relative-movement damage. సమాధానం: B.
-
Question 23 ప్రశ్న 23Answer: C. 20 N. సమాధానం: C.
-
Question 24 ప్రశ్న 24Answer: D. 72 MPa. సమాధానం: D.
-
Question 25 ప్రశ్న 25Answer: B. Part 1 — General Provisions; Part 2 — Block Foundations; Part 3 — Frame Foundations; Part 4 — Foundations for Hammers and Presses. సమాధానం: B.