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PEB Singapore PPE Mechanical practice questions

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Question 1Mechanical Engineering Design and Analysis

A simply supported beam of span L carries a single concentrated load W at midspan. The maximum bending moment in the beam is:

  1. WL²/8
  2. WL/2
  3. WL/8
  4. WL/4 Correct answer.

Explanation

The reactions at each support are W/2, so the bending moment diagram is triangular with its peak at midspan, giving M = (W/2)(L/2) = WL/4.

Question 2Mechanical Engineering Design and Analysis

A component made from a metal with a yield strength of 240 MPa is designed to operate at a maximum working stress of 120 MPa. The factor of safety on yield is:

  1. 120
  2. 2.0 Correct answer.
  3. 0.5
  4. 240

Explanation

The factor of safety is the ratio of the limiting strength to the actual working stress, so 240 MPa divided by 120 MPa gives 2.0.

Question 3Mechanical Engineering Design and Analysis

Within the linear-elastic range, which expression correctly relates axial stress σ, axial strain ε and Young's modulus E?

  1. σ = E/ε
  2. E = σε
  3. σ = Eε Correct answer.
  4. ε = Eσ

Explanation

Hooke's law in one dimension states that stress is directly proportional to strain, with Young's modulus as the constant of proportionality, hence σ = Eε.

Question 4Mechanical Engineering Design and Analysis

For a ductile metal subjected to a general three-dimensional state of static stress, the most appropriate yield criterion is:

  1. von Mises theory Correct answer.
  2. Mohr–Coulomb theory
  3. Maximum principal strain theory
  4. Maximum principal stress theory

Explanation

The von Mises (maximum distortion energy) criterion matches experimental yielding of ductile metals closely, because yielding is driven by distortion energy rather than by a single principal stress.

Question 5Mechanical Engineering Design and Analysis

For a centrifugal pump with unchanged impeller diameter, doubling the rotational speed will cause the flow rate at the best efficiency point to:

  1. remain the same
  2. increase by a factor of eight
  3. double Correct answer.
  4. quadruple

Explanation

The affinity laws state that capacity varies directly with rotational speed, so doubling the speed doubles the flow at the best efficiency point.

Question 6Mechanical Engineering Design and Analysis

The natural frequency in hertz of an undamped single-degree-of-freedom spring-mass system is given by:

  1. √(m/k)/(2π)
  2. √(k/m)/(2π) Correct answer.
  3. 2π√(m/k)
  4. 2π√(k/m)

Explanation

The angular natural frequency is ω = √(k/m) rad/s, and converting to hertz requires dividing by 2π, giving f = √(k/m)/(2π).

Question 7Mechanical Engineering Design and Analysis

The main purpose of preloading a bolted joint that carries a cyclic load is to:

  1. reduce the bolt proof strength
  2. allow the joint to slip under shear
  3. lower the cyclic bolt stress range Correct answer.
  4. eliminate the need for washers

Explanation

High preload clamps the joint so that the external cyclic load is shared mainly between the clamped parts, reducing the alternating stress seen by the bolt and improving fatigue life.

Question 8Mechanical Engineering Design and Analysis

The basic rating life L10 of a rolling element bearing is defined as the life that:

  1. 50% of a group of identical bearings will attain or exceed
  2. 90% of a group will attain or exceed Correct answer.
  3. 90% of a group will fail to reach
  4. is reached at the first sign of fatigue

Explanation

L10 is a statistical rating: it is the life reached or exceeded by 90% of a sufficiently large group of apparently identical bearings before fatigue spalling occurs.

Question 9Mechanical Engineering Design and Analysis

A solid circular shaft of 50 mm diameter transmits a torque of 1.0 kN·m. The maximum shear stress in the shaft is closest to:

  1. 81.5 MPa
  2. 13.6 MPa
  3. 20.4 MPa
  4. 40.7 MPa Correct answer.

Explanation

For a solid circular shaft τ = 16T/(πd³), so 16 × 1000 divided by (π × 0.05³) gives approximately 40.7 MPa.

Question 10Mechanical Engineering Design and Analysis

A pin-ended steel column of length L buckles at an elastic critical load of 200 kN. If the length is doubled while the cross-section is unchanged, the critical load becomes:

  1. 400 kN
  2. 25 kN
  3. 100 kN
  4. 50 kN Correct answer.

Explanation

The Euler buckling load is inversely proportional to the square of the effective length, so doubling the length reduces the critical load by a factor of four, giving 50 kN.

Question 11Mechanical Engineering Design and Analysis

Which statement about the theoretical stress concentration factor Kt is correct?

  1. It relates the peak local elastic stress to the nominal stress Correct answer.
  2. It equals the fatigue notch factor for all notch radii
  3. It is independent of the notch geometry
  4. It applies directly to ductile materials under static load without modification

Explanation

Kt is defined as the ratio of the peak elastic stress at a discontinuity to the nominal stress on the net section, evaluated with the part treated as fully elastic.

Question 12Mechanical Engineering Design and Analysis

Under a fluctuating stress with a non-zero tensile mean stress, the Goodman relation predicts that the allowable alternating stress:

  1. is independent of the mean stress level
  2. equals the ultimate strength at zero mean stress
  3. increases linearly with mean stress
  4. decreases linearly with increasing mean stress Correct answer.

Explanation

The Goodman line runs from the endurance limit on the alternating-stress axis to the ultimate tensile strength on the mean-stress axis, so allowable alternating stress falls linearly as mean stress rises.

Question 13Mechanical Engineering Design and Analysis

A closed thin-walled cylindrical pressure vessel has internal pressure p, internal diameter D and wall thickness t, with t much smaller than D. The hoop stress in the wall is:

  1. pD/t
  2. pD/(2t) Correct answer.
  3. 2pD/t
  4. pD/(4t)

Explanation

Balancing the bursting force on a longitudinal half-section against the resisting wall area gives a hoop stress of pD/(2t) for the thin-wall approximation.

Question 14Mechanical Engineering Design and Analysis

Two spur gears mesh. For a given face width, the torque the teeth can transmit is governed mainly by the module because the module determines:

  1. the number of teeth on each gear
  2. the tooth size and bending strength Correct answer.
  3. the pressure angle at the pitch point of the mesh
  4. the centre distance required for a given ratio

Explanation

Module fixes the physical size of the tooth for a given tooth count, and tooth bending strength scales with the square of tooth size, so module is the primary driver of torque capacity per unit face width.

Question 15Mechanical Engineering Design and Analysis

For an equal-leg fillet weld of leg length a, the throat thickness used to compute stresses on the weld is:

  1. 0.707a Correct answer.
  2. 1.414a
  3. 0.5a
  4. a

Explanation

The critical section of a 90° fillet weld runs from the root to the face at 45°, so the throat thickness equals a times cos 45°, that is 0.707a.

Question 16Mechanical Engineering Design and Analysis

A square key of width w and length L on a shaft of diameter d transmits a torque T. The average shear stress in the key is:

  1. 2T/(wLd) Correct answer.
  2. T/(wLd)
  3. T/(2wLd)
  4. 4T/(wLd)

Explanation

The tangential force on the key is T divided by the shaft radius, giving 2T/d, and dividing by the shear area wL gives an average shear stress of 2T/(wLd).

Question 17Mechanical Engineering Design and Analysis

Two helical compression springs of stiffness k1 and k2 are arranged in series. The equivalent stiffness of the combination is:

  1. k1k2/(k1+k2) Correct answer.
  2. (k1+k2)/2
  3. 1/k1 + 1/k2
  4. k1+k2

Explanation

In series the same force passes through both springs and the deflections add, so the compliances add and the equivalent stiffness is the product over the sum, k1k2/(k1+k2).

Question 18Mechanical Engineering Design and Analysis

For flow in a circular pipe, the transition from laminar to turbulent flow occurs in the region of Reynolds number:

  1. 20000 to 40000
  2. 200
  3. 200000
  4. 2000 to 4000 Correct answer.

Explanation

Pipe flow is reliably laminar below about 2000 and fully turbulent above about 4000, with the critical transition region lying between these values.

Question 19Mechanical Engineering Design and Analysis

A steel bar fully restrained at both ends is heated uniformly through a temperature rise ΔT. The compressive stress developed in the bar is:

  1. EαΔT/L
  2. EαΔT Correct answer.
  3. αΔT/E
  4. EαΔT·L

Explanation

Full restraint suppresses the free thermal strain αΔT, so the elastic strain required to restore compatibility is αΔT and the stress is E times that strain.

Question 20Mechanical Engineering Design and Analysis

In the ISO hole-basis system of limits and fits, a transition fit is one in which:

  1. clearance is always positive
  2. interference is always positive
  3. the hole zone lies below the shaft
  4. the zones overlap Correct answer.

Explanation

In a transition fit the tolerance zones of the hole and shaft overlap, so depending on the actual sizes produced the assembly may have a small clearance or a small interference.

Question 21Mechanical Engineering Design and Analysis

A solid circular shaft of diameter d is subjected simultaneously to a bending moment M and a torque T. According to the maximum distortion energy criterion, the equivalent von Mises stress is:

  1. (16/πd³)√(M² + 0.75T²) Correct answer.
  2. (16/πd³)√(M² + T²)
  3. (16/πd³)(M + T)
  4. (32/πd³)√(M² + T²)

Explanation

Bending gives a normal stress 32M/(πd³) and torsion a shear stress 16T/(πd³); substituting these into the von Mises expression reduces to (16/πd³) times the square root of (M² + 0.75T²).

Question 22Mechanical Engineering Design and Analysis

A shaft shoulder has a theoretical stress concentration factor Kt of 2.4. For the shoulder radius used, the notch sensitivity q is 0.8. The fatigue notch factor Kf is:

  1. 2.40
  2. 3.00
  3. 1.92
  4. 2.12 Correct answer.

Explanation

The fatigue notch factor is obtained from Kf = 1 + q(Kt − 1), which gives 1 + 0.8 × 1.4 = 2.12.

Question 23Mechanical Engineering Design and Analysis

A rotor of mass 200 kg is mounted at midspan of a shaft whose local stiffness is 4 MN/m. Neglecting shaft mass, the first critical speed is closest to:

  1. 675 rpm
  2. 955 rpm
  3. 1350 rpm Correct answer.
  4. 2700 rpm

Explanation

The angular natural frequency is √(k/m) = √(4×10⁶/200) ≈ 141.4 rad/s, and multiplying by 60/(2π) gives approximately 1350 rpm.

Question 24Mechanical Engineering Design and Analysis

In the shell thickness formula of ASME Section VIII Division 1, the joint efficiency E accounts for:

  1. the corrosion allowance added to the calculated thickness
  2. the strength of the weld filler metal relative to the base metal
  3. the reduction in allowable stress at elevated temperature
  4. the strength reduction allowed for welded joints Correct answer.

Explanation

The joint efficiency is a quality factor, never greater than unity, that discounts the shell strength to reflect the type and extent of radiographic examination of the longitudinal welded seams.

Question 25Mechanical Engineering Design and Analysis

For a flat belt drive at the point of slipping, and neglecting centrifugal effects, the ratio of tight-side to slack-side tension is governed by:

  1. The initial tension and the belt mass per unit length
  2. The belt speed and the pulley diameter
  3. The coefficient of friction and the angle of lap Correct answer.
  4. The belt width and the belt thickness

Explanation

At impending slip the belt friction relation T1/T2 = e^(μθ) applies, where μ is the coefficient of friction between belt and pulley and θ is the angle of lap in radians. Belt width, thickness, speed and initial tension affect the power capacity, but they do not set the limiting tension ratio itself.

Question 26Mechanical Engineering Design and Analysis

A deep-groove ball bearing carries a radial load Fr and an axial load Fa at the same time. In the basic rating life equation the equivalent dynamic load P is obtained from:

  1. P = X·Fr + Y·Fa with tabulated factors Correct answer.
  2. P = the square root of (Fr squared plus Fa squared)
  3. P = the larger of Fr and Fa
  4. P = Fr + Fa

Explanation

Rolling bearings under combined loading use the equivalent dynamic load P = X·Fr + Y·Fa, where the radial factor X and thrust factor Y are taken from the bearing catalogue for the relevant Fa/Fr ratio. This weighted sum reflects that axial load is carried less efficiently than radial load in a deep-groove bearing.

Question 27Mechanical Engineering Design and Analysis

A multi-plate friction clutch has 4 pairs of friction surfaces, a coefficient of friction of 0.3 and a total axial clamping force of 2 kN. The friction lining has outer radius 200 mm and inner radius 100 mm and the uniform-wear assumption applies. The torque capacity is closest to:

  1. 90 N·m
  2. 720 N·m
  3. 180 N·m
  4. 360 N·m Correct answer.

Explanation

Under uniform wear the effective friction radius is the mean radius, (ro + ri)/2 = 150 mm, and each pair of surfaces transmits torque μ·W·r_mean with the full clamping force W. Hence T = n·μ·W·r_mean = 4 × 0.3 × 2000 × 0.15 = 360 N·m.

Question 28Mechanical Engineering Design and Analysis

A closed thick-walled cylinder has internal radius 50 mm and external radius 100 mm, and carries an internal pressure of 20 MPa with zero external pressure. The maximum hoop stress, which occurs at the bore, is closest to:

  1. 30.0 MPa
  2. 33.3 MPa Correct answer.
  3. 26.7 MPa
  4. 20.0 MPa

Explanation

Lamé's solution gives the peak hoop stress at the bore as p·(ro² + ri²)/(ro² − ri²). Substituting gives 20 × (10000 + 2500)/(10000 − 2500) = 20 × 1.667 = 33.3 MPa.

Question 29Mechanical Engineering Design and Analysis

A flywheel of mass moment of inertia 10 kg·m² runs at a mean speed of 300 rev/min with a coefficient of fluctuation of speed of 0.02. The maximum fluctuation of energy is closest to:

  1. 19.7 J
  2. 197 J Correct answer.
  3. 99 J
  4. 395 J

Explanation

The energy fluctuation is related to inertia by ΔE = I·ω²·Cs, where ω is the mean angular velocity. With ω = 2π × 300/60 = 31.4 rad/s, ΔE = 10 × 987 × 0.02 ≈ 197 J.

Question 30Mechanical Engineering Design and Analysis

A component is subjected to a repeated block of loading: 20 000 cycles at a stress level for which the allowable number of cycles is 100 000, followed by 10 000 cycles at a stress level for which the allowable number is 25 000. Applying the Palmgren–Miner linear damage rule, the fraction of fatigue life still unused after one block is:

  1. 0.60
  2. 0.50
  3. 0.80
  4. 0.40 Correct answer.

Explanation

Miner's rule sums the damage fractions n/N for each stress level: 20 000/100 000 + 10 000/25 000 = 0.20 + 0.40 = 0.60. Failure is predicted when the sum reaches unity, so the unused fraction of life is 1 − 0.60 = 0.40.

Question 31Building Services and HVAC Systems

Relative humidity is defined as the ratio of the actual water vapour pressure in the air to the:

  1. saturation vapour pressure at the dew point
  2. saturation vapour pressure at the room's design condition
  3. saturation vapour pressure at the same temperature Correct answer.
  4. total pressure of the moist air mixture

Explanation

Relative humidity compares the water vapour actually present with the maximum the air could hold at that same dry-bulb temperature, expressed as a percentage. Because the comparison is made at the same temperature, the denominator is the saturation vapour pressure at that temperature.

Question 32Building Services and HVAC Systems

Which of the following contributes to the latent cooling load of an occupied space?

  1. solar radiation through the glazing
  2. heat given off by lighting and equipment
  3. heat conducted through the external wall
  4. moisture released by occupants and processes Correct answer.

Explanation

Latent load is the heat that must be removed to condense water vapour, so it arises from moisture sources such as people, cooking, washing and infiltration of humid outdoor air. Solar gain, conduction and internal equipment heat all change dry-bulb temperature and are therefore sensible loads.

Question 33Building Services and HVAC Systems

A centrifugal fan runs at 1.5 times its original speed while the system resistance curve stays unchanged. The static pressure developed becomes:

  1. 2.25 times the original Correct answer.
  2. 1.22 times the original
  3. 3.00 times the original
  4. 1.5 times the original

Explanation

Fan laws state that at constant air density, static pressure varies with the square of the speed while airflow varies linearly and power with the cube. Squaring 1.5 gives 2.25.

Question 34Building Services and HVAC Systems

The purpose of the outdoor-air intake in an air-conditioned office is to:

  1. reduce the refrigeration load on the chillers
  2. humidify the occupied space during dry periods
  3. lower the supply air temperature delivered to the space
  4. dilute indoor contaminants and replenish oxygen Correct answer.

Explanation

Outdoor air is introduced for indoor air quality: it dilutes body odours, carbon dioxide, volatile organic compounds and other pollutants and replaces the oxygen consumed by occupants. It is a penalty on the cooling plant rather than a benefit.

Question 35Building Services and HVAC Systems

Which of these refrigerants contains chlorine and therefore has a non-zero ozone depletion potential?

  1. R-134a
  2. R-410A
  3. R-22 Correct answer.
  4. R-407C

Explanation

Ozone depletion is caused by chlorine (or bromine) atoms released when the molecule breaks down in the stratosphere. R-22 is an HCFC containing chlorine, so it has a measurable ODP and is being phased out.

Question 36Building Services and HVAC Systems

In a water-cooled chilled-water plant, the component that rejects heat from the condenser water to the atmosphere is the:

  1. primary chilled-water pump
  2. cooling tower Correct answer.
  3. chiller evaporator
  4. air handling unit

Explanation

The chiller transfers heat from the chilled water to the condenser water, and the cooling tower then rejects that heat to the atmosphere through evaporation and sensible exchange. The tower is the final heat sink of the plant.

Question 37Building Services and HVAC Systems

A fire damper installed where a duct penetrates a fire-rated wall is provided to:

  1. reduce noise transmission between the rooms
  2. modulate airflow to suit the zone demand
  3. balance the air quantities in the branch ducts
  4. close to preserve the fire rating of the wall Correct answer.

Explanation

A fire damper is a fire-protection device that closes on a rise in temperature or a fire signal so the duct opening does not allow fire to pass through a fire-rated element. It holds the integrity of the compartmentation, not the air balance.

Question 38Building Services and HVAC Systems

A condensate trap is fitted to the drain of a cooling coil mainly to:

  1. measure the condensate flow rate for the water balance
  2. prevent algal growth in the drain pipe
  3. drain condensate while preventing air leakage through the pipe Correct answer.
  4. filter dust and dirt from the condensate before discharge

Explanation

Because the coil is under negative or positive pressure relative to the drain, a water seal (trap) is needed so that condensate can run away while air is not drawn in or blown out. The trap depth is sized from the fan static pressure plus a margin.

Question 39Building Services and HVAC Systems

Air enters a cooling coil at 25 °C dry bulb and leaves at 12.5 °C dry bulb, with an apparatus dew point of 10 °C. The coil contact factor is:

  1. 0.60
  2. 0.95
  3. 0.72
  4. 0.83 Correct answer.

Explanation

Contact factor is the ratio of the actual dry-bulb drop to the drop that would occur if the air reached the apparatus dew point: (25 − 12.5) / (25 − 10) = 0.83. A value below 1 indicates that some air bypasses the coil surface.

Question 40Building Services and HVAC Systems

The equal-friction method of duct sizing selects duct dimensions so that every section has the same:

  1. air velocity in metres per second
  2. pressure loss per metre of length Correct answer.
  3. velocity pressure at the branch take-off
  4. aspect ratio of width to height

Explanation

In the equal-friction method the designer picks a constant pressure gradient, typically 0.8 to 1.2 Pa/m, and reads the duct size that gives that loss at the design airflow. Velocity then falls naturally as the air quantity reduces along the run.

Question 41Building Services and HVAC Systems

A pump driven by a variable-speed drive is slowed to 80% of its design speed with no change to the system curve. The absorbed power falls to approximately:

  1. 80% of design
  2. 51% of design Correct answer.
  3. 64% of design
  4. 40% of design

Explanation

Pump power follows the cube of speed for a fixed system, so 0.8 cubed is 0.512. The saving is proportionally much larger than the reduction in speed or flow.

Question 42Building Services and HVAC Systems

A chiller delivers 500 kW of cooling while drawing 100 kW of electrical input. Its coefficient of performance is:

  1. 4.0
  2. 0.2
  3. 6.0
  4. 5.0 Correct answer.

Explanation

COP is cooling output divided by work input, i.e. 500 / 100 = 5.0. It is a dimensionless ratio and can exceed 1 because the chiller moves heat rather than creating cooling.

Question 43Building Services and HVAC Systems

In a variable air volume system, the room temperature at part load is maintained mainly by:

  1. opening the outdoor-air damper wider
  2. changing the chilled-water flow through the coil
  3. switching the supply fan on and off
  4. reducing the volume of cool air supplied Correct answer.

Explanation

A VAV terminal box throttles the quantity of constant-temperature primary air entering the zone, so the sensible capacity drops as the load falls. The supply fan and central plant then respond to duct static pressure to save energy.

Question 44Building Services and HVAC Systems

The approach of a cooling tower is the difference between the:

  1. entering air dry-bulb and wet-bulb temperatures
  2. hot water temperature and the ambient dry-bulb temperature
  3. entering and leaving water temperatures across the tower
  4. leaving water temperature and the entering air wet-bulb temperature Correct answer.

Explanation

Approach is how close the cold water comes to the entering air wet-bulb temperature, and it governs the tower size for a given duty. The difference between the hot and cold water temperatures is the range, not the approach.

Question 45Building Services and HVAC Systems

For a fixed cooling load, increasing the design chilled-water temperature difference across the coils will:

  1. reduce the required flow rate Correct answer.
  2. reduce the chiller capacity
  3. increase the required flow rate
  4. have no effect on the flow rate

Explanation

Cooling load equals mass flow times specific heat times temperature difference, so a larger ΔT allows a smaller flow for the same load. Smaller flow means smaller pipes and pumps and lower pumping energy, at the cost of a colder supply or warmer return.

Question 46Building Services and HVAC Systems

A stair pressurisation system in a high-rise building is designed to:

  1. hold the stair at a positive pressure Correct answer.
  2. cool the stair enclosure during a fire
  3. extract smoke directly from the stair landing
  4. supply outside air to the lift lobby only

Explanation

Forcing air into the escape stair keeps it at a pressure above the adjacent fire floor so that smoke cannot leak in through closed doors. The pressure must be limited, typically 20 to 50 Pa, so that the door opening force stays within limits.

Question 47Building Services and HVAC Systems

Condensation will form on the outside of an uninsulated chilled-water pipe when the pipe surface temperature is:

  1. below the dry-bulb of the surrounding air
  2. below the dew point of the surrounding air Correct answer.
  3. equal to the dry-bulb of the surrounding air
  4. above the wet-bulb of the surrounding air

Explanation

Moisture condenses whenever a surface is colder than the dew point of the adjacent air, which is why chilled-water pipework and drains must be vapour-sealed and insulated. Surface temperature below dry bulb but above dew point only gives sensible cooling.

Question 48Building Services and HVAC Systems

Air flowing at 8 m/s in a duct where the density is 1.2 kg/m³ has a velocity pressure of about:

  1. 19 Pa
  2. 38 Pa Correct answer.
  3. 77 Pa
  4. 96 Pa

Explanation

Velocity pressure equals one half of density times velocity squared: 0.5 × 1.2 × 8² = 38.4 Pa. This value is used to convert between static, velocity and total pressure at a measurement section.

Question 49Building Services and HVAC Systems

Chilled-water velocities in large distribution mains are normally kept within about 1.5 to 2.5 m/s mainly to:

  1. allow the use of smaller automatic air vents
  2. keep the water in the turbulent regime
  3. prevent the water temperature from rising in the pipe
  4. limit erosion, noise and pressure drop Correct answer.

Explanation

Excessive velocity causes erosion-corrosion at fittings, noise and a steep rise in friction loss, which drives pump energy up. Keeping the mains within this band balances pipe cost against pumping and noise.

Question 50Building Services and HVAC Systems

The face velocity across a cooling coil is usually limited to about 2.5 m/s in order to:

  1. avoid condensate being carried into the ductwork Correct answer.
  2. increase the coil's latent capacity
  3. prevent the coil from freezing
  4. reduce the chilled-water pressure drop

Explanation

High face velocity strips droplets from the wet coil surface and carries them downstream, causing wet ducts and microbial problems. The limit also keeps the air-side pressure drop reasonable.