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Adding the shear stress directly to the larger normal stress gave 110 MPa. Principal stress comes from Mohr-circle geometry and was only 92.4 MPa.
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Practice now β FE DISCIPLINE10 practice questions available
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Adding the shear stress directly to the larger normal stress gave 110 MPa. Principal stress comes from Mohr-circle geometry and was only 92.4 MPa.
The polar moment was correct, but shear stress was evaluated at half the outer radius. Maximum torsional stress occurs at the outside surface and was 50.9 MPa.
The stress was correct, but only half the member length was used in the deformation equation. The full bar stretched 0.80 mm.
The hydraulic gradient was correct, but the plan-view area was used instead of the area perpendicular to groundwater flow. The aquifer moved 1,500 ftΒ³/day.
The basin received 21,600 ftΒ³ during the design interval, but 9,000 ftΒ³ left through the outlet at the same time. Required storage was only the net 12,600 ftΒ³.
The rainfall intensity and drainage area were correct, but the runoff coefficient was omitted. The design peak runoff was 60.5 cfs, not 100.8 cfs.
The geometric concrete volume was 74.1 ydΒ³, but the purchase order had to include 8% waste. The correct order quantity was 80 ydΒ³.
Actual cost was divided by earned value, producing 1.33 and a false impression of good performance. CPI is EV/AC, so the project was only at 0.75.
The shorter branch finished in 12 days, but project completion waited on the longer A-B-D-F path. The correct duration was 16 days.
The project generated 306 total trips in the PM peak hour, but only 65% were entering. The inbound design demand was about 199 veh/h.
The spacing was 132 ft per vehicle, but 45 mph was treated as 45 ft/s. Correct unit conversion gives density 40 veh/mi and flow 1,800 veh/h/lane.
The design speed was correct, but superelevation was omitted. Including both superelevation and side friction reduced the required curve radius to about 833 ft.
Using only the surcharge term gave 331 kPa. The width-dependent soil-weight term raised the gross ultimate bearing capacity to about 614 kPa.
Total overburden at 7 m was 134 kPa, but pore water carried 39.2 kPa. The soil skeleton carried only 94.8 kPa effective stress.
Using wet density as dry density produced e=0.50. Correcting for 20% water content gave e=0.80 and 67.5% saturation.
Material A had the higher yield strength, but its density penalty was much larger. After sizing both rods to the same factor of safety, Material B produced the lighter design.
The resistivity formula was correct, but 2 mmΒ² was treated as 2Γ10^-9 mΒ² instead of 2Γ10^-6 mΒ². The wire resistance was 0.17 ohm.
The thermal strain was correct, but it was applied as if the bar were only 1 m long. The 2 m bar expanded 2.3 mm.
Dividing the overall composition by the beta composition gave 57%, but phase fractions come from tie-line segment lengths. The beta fraction was 40%.
The outcomes were not equally likely. Probability-weighting gives an expected value of $52,000, not the simple average of $35,000.
The fixed-cost difference was correct, but break-even depends on the difference in variable costs. The correct crossover is 10,000 units.
Undiscounted cash flows suggested a $25,000 gain; discounted NPV is about $3,675.
The vessel pressure was 700 kPa absolute, but the valve disk also had atmospheric pressure acting on the opposite side. Net pressure force depended on the 600 kPa differential.
Eighteen hours represented three half-lives, not two. A 240-unit rate therefore fell to 30, not 60.
Six air changes per hour sounded like 1,080 mΒ³/min when the hour-to-minute conversion was skipped. The required flow was 18 mΒ³/min.
A 5% defective process did not imply a 95% lot-acceptance probability. Under an n=20, c=1 plan, acceptance required observing zero or one defective item.
Quality loss did not grow linearly with deviation from target. Under the Taguchi quadratic model, a 3-unit deviation caused a $45 loss.
The process spread fit comfortably inside the specification width, but the mean had shifted toward the USL. Cp looked strong while Cpk exposed the centering problem.
The individual-process spread looked wide enough to contain 53.5, but an xΜ chart uses the standard error of the sample mean. The upper control limit was 53.0.
Site A had the higher simple average freight rate, but most demand was on its low-cost lane. Demand-weighted annual cost made Site A $10,000 cheaper.
Three machines looked sufficient at 100% theoretical availability. At the planned 80% utilization, the cell required four machines.
Layout A had the shorter average distance, but its busiest material-flow pair was much farther apart. Weighted load-distance made Layout B the better design.
Ordering the full annual demand once minimized ordering frequency, not total inventory cost. The EOQ was about 707 units.
The latest actual demand was 130 units, but exponential smoothing with Ξ±=0.30 did not replace the forecast with 130. The next forecast became 109.
The arithmetic produced 3.6 stations, but a production line cannot operate with a fraction of a station. The theoretical minimum was 4.
Averaging 8% and 1% gave 4.5%, but the two waste streams had different masses. The correct mixed concentration was 5.67% by mass.
An outlet of 0.025 kg/hr from a 25 kg/hr hazardous constituent feed means only 0.1% remains. The destruction/removal efficiency is 99.9%.
Precipitation minus evapotranspiration was not enough. Runoff and storage change reduced the annual leachate estimate to 12,000 mΒ³.
Ignoring daily cover made the landfill appear to last 4.11 years. Including 20% cover-volume use reduced the life to about 3.42 years.
A 70% cyclone followed by an 80% baghouse did not provide 150% removal. The second device treated only what escaped the first, giving 94% overall removal.
Dividing generation by room volume produced a concentration rise rate. The steady indoor concentration was controlled by ventilation and reached 6.5 mg/mΒ³.
The scrubber removed 36 lb/hr, but that was not the stack emission. Only 4 lb/hr remained after 90% control.
The hydraulic detention time was 30 minutes, but baffling reduced the effective contact time to 21 minutes. The CT value was 31.5, not 45.
Splitting the flow between two clarifiers did not halve the total required area. The system still needed 12,000 ftΒ² in service.
The concentration drop was 210 mg/L, but that was not a mass removal rate. At 2.5 MGD, the plant removed about 4,379 lb/day of BOD.
Seventy percent of A reacted, but only fifty percent of the feed became the desired product B. Conversion was not the same as yield.
A 30 K temperature rise did not cause a 10% kinetic change. The Arrhenius relation increased the rate constant by a factor of about 6.19.
The PFR-sized volume looked efficient, but the well-mixed CSTR needed 600 L to reach the same 60% conversion.
The shortcut kt=1 suggested 100% conversion after 5 minutes. The first-order batch model gave only 63.2%.
The reactant methane formation enthalpy was only -74.8 kJ/mol. The balanced combustion released nearly 890 kJ/mol.
No heater was attached, yet adiabatic reversible compression raised the ideal-gas temperature from 300 K to about 446 K.
A binary liquid did not boil when total pressure equaled either pure-component vapor pressure. Its bubble pressure was the composition-weighted sum.
Heating the liquid required 209 kJ/kg. At 2 kg/s, that became 418 kW of heat transfer.
The feed was 1000 kg/h at 10 wt% solids. Concentrating to 40 wt% left only 250 kg/h liquid product.
A 10 wt% stream and a 40 wt% stream had to produce 25 wt% product. The concentrate flow was 100 kg/h, not 25.
The shaft power was 30 kW at 1200 rpm. That meant about 239 NΒ·m torque, not 30 NΒ·m.
At 2 MPa internal pressure, the vessel's hoop stress reached 100 MPaβtwice the longitudinal stress.
The spring force was 500 N, but the deflection depended strongly on wire diameter, coil diameter, and active coils.
The torque was only 2 kNΒ·m, but the outer surface of the 50 mm shaft reached about 81.5 MPa shear stress.
The water received 9.81 kW. A 70% efficient pump required about 14.0 kW of shaft input.
The velocity stayed at 2 m/s, yet wall friction consumed 20 kPa of pressure over the pipe length.
The oil was moving at 2 m/s, but its Reynolds number was only 1700.
The refrigerator removed 6 kW of heat using 2 kW of work. A COP of 3 was correct, not impossible.
The turbine power came from a 600 kJ/kg enthalpy drop, not from subtracting internal energies blindly.
The gas temperature rose from 300 K to 450 K. The pressure did not scale with Celsius temperature.
The flow area alone was not enough. Hydraulic radius and slope set the channel discharge.
The pipe stayed level. Velocity increased from 2 to 6 m/s, and pressure fell from 300 to 284 kPa.
The diameter fell by half. The velocity did not merely doubleβit rose from 1.5 to 6.0 m/s.
The water was motionless, but pressure still increased with depth.
The steel strength was not the first limit. Slender-column instability governed near 497 kips.
The total load was 30 kips. Multiplying by half the span produced the wrong bending moment.
The floor load was 50 psf. The beam did not carry 50 lb/ftβit carried 400 lb/ft.
Each support reaction was only 6 kN, yet each inclined top member carried about 8.49 kN.
The total load was 28 kN, but the support reactions were not 14 kN each.
A 10 kN load was shared by two cables, but each cable still carried 10 kN of tension.
Two routes matched the destination. The router chose the more specific prefix, not the visually simpler route.
Serialization took only 12 microseconds. The fiber path added another 500 microseconds.
The subnet looked large enough from the address range. The usable host count said otherwise.
Four 20 kHz channels looked like an 80 kHz jobβuntil the guard bands were counted.
The voice channel bandwidth was 4 kHz. The data link was sized at 32 kbps and immediately overflowed.
The carrier was 5 V. The message amplitude was 6 V. The envelope detector stopped reproducing the message cleanly.
Increasing gain improved responseβuntil the characteristic equation crossed the stability limit.
The low-frequency gain was 40 dB. One decade past the pole, the response was near 20 dB.
The forward gain was 10. The closed-loop output did not become 10 times the reference.
The secondary load was 8 Ξ©. The primary source did not see 8 Ξ©βor even 32 Ξ©.
The source measured 240 V. The load saw only 228 V because the feeder resistance was treated as one-way.
The load was only 30 kW, but the feeder current was much higher than the kW-only calculation predicted.
The gain equation requests -10 V, but the amplifier only has Β±5 V rails.
An NPN switch has VCC = 5 V, Rc = 100 Ξ©, Ξ² = 100, and Ib = 1 mA. Ξ²Ib predicts 100 mA, but with VCE(sat) β 0.2 V the collector circ
The reverse-polarity protection worked, but the 5 V sensor would not start.
A perfect step arrived. The filter answered 2.0 instead of 10.
A 'passband' tone reached the cutoff and lost nearly 30% of its amplitude.
The machine says 900 Hz. The sampled spectrum insists on 300 Hz.
The numerator says 20. The unit-step output settles at 5. The model is working exactly as written.
Both reactive components looked like opposition. At resonance, they canceled and the current doubled the protection limit.
The steady-state current is zero. At switch-on, the circuit violates its 5 mA startup limit.
The divider measured exactly 6 V with no load. Connect one load, and the output falls to 4 V.
Each branch looked safe. The supply still tripped the instant the second load was connected.
A 12 V source is connected across a required 2 Ξ© load. The calculated and measured current is 6 A, but the resistor overheats and fails within seconds. Identify the missing engineering check, prove the root cause, and choose a safe correction.
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