CENEVAL EGEL Plus Ingeniería Mecánica (EGEL Plus IMECA)

A simply supported horizontal beam of length L = 6.0 m carries a concentrated downward load of P = 12 kN at a distance of 2.0 m from the left support A. Assuming no horizontal forces, what is the vertical reaction force at the right support B?

• A4.0 kN
• B8.0 kN
• C6.0 kN
• D24.0 kN

A cart with a total mass of m = 500 kg is accelerated horizontally along a straight track at a constant acceleration of a = 3.0 m/s². Using D'Alembert's principle of dynamic equilibrium, what is the magnitude of the fictitious inertia force acting on the cart in the direction opposite to acceleration?

• A1,500 N
• B4,905 N
• C166.7 N
• D6,405 N

In a planar four-bar linkage, the lengths of the links are: shortest link s = 30 mm, longest link l = 90 mm, and the two intermediate links p = 50 mm and q = 80 mm. According to Grashof's criterion, what type of mechanism is formed when the shortest link s is fixed to the ground frame?

• ADouble-crank (drag-link) mechanism
• BCrank-rocker mechanism
• CDouble-rocker mechanism
• DNon-Grashof (triple-rocker) mechanism

In the kinematic analysis of a planar rigid body moving in a plane, how is the instantaneous center of zero velocity (ICZV) defined?

• AThe point in the body or its extension that has zero linear velocity at a specific instant
• BThe point where both linear velocity and linear acceleration are simultaneously zero
• CThe center of gravity of the rigid body where all external dynamic forces act
• DThe fixed geometric pivot around which the mechanism rotates throughout its entire cycle

A solid circular bar with a cross-sectional area A = 500 mm² and section modulus Z = 5,000 mm³ is subjected simultaneously to a tensile axial force P = 50 kN and a bending moment M = 150 N·m. What is the maximum normal tensile stress on the outer fibers?

• A130 MPa
• B100 MPa
• C30 MPa
• D70 MPa

A 2D element is subjected to normal stresses σ_x = 80 MPa, σ_y = -20 MPa, and shear stress τ_xy = 0. What is the maximum in-plane shear stress τ_max in this element?

• A50 MPa
• B30 MPa
• C100 MPa
• D60 MPa

A turned shaft is specified as 25.00 ± 0.05 mm (LSL = 24.95 mm, USL = 25.05 mm). A capability study of the stable process gives a mean of 25.01 mm and a standard deviation σ = 0.01 mm. What are the process capability indices Cp and Cpk?

• ACp ≈ 1.67, Cpk ≈ 1.33
• BCp ≈ 1.67, Cpk ≈ 2.00
• CCp ≈ 3.33, Cpk ≈ 2.67
• DCp ≈ 1.33, Cpk ≈ 1.67

According to Lamé's equations for a thick-walled cylinder subjected solely to internal gauge pressure p_i with inner radius r_i and outer radius r_o, at which location does the maximum tangential (hoop) tensile stress occur?

• AAt the inner surface (r = r_i)
• BAt the outer surface (r = r_o)
• CAt the geometric mid-radius (r = (r_i + r_o) / 2)
• DUniformly distributed across the entire wall thickness

When designing machine components manufactured from ductile steel under plane stress conditions, how does the safe design region predicted by the Maximum Shear Stress (Tresca) theory compare to that of the Distortion Energy (von Mises) theory?

• ATresca is a hexagon inscribed inside the von Mises ellipse, making Tresca more conservati…
• BTresca is an ellipse circumscribed outside the von Mises hexagon, making Tresca less cons…
• CTresca and von Mises yield identical envelopes across all stress quadrants
• DTresca is more conservative only in pure hydrostatic compression but less conservative in…

A cylindrical shaft is subjected to a pure normal bending stress σ = 120 MPa and a torsional shear stress τ = 40 MPa at its critical point. What is the von Mises equivalent stress σ_v?

• A138.6 MPa
• B160.0 MPa
• C126.5 MPa
• D144.2 MPa

Which failure criterion is recommended for designing structural components made of brittle materials (such as gray cast iron) that exhibit significantly higher ultimate compressive strength (S_uc) than ultimate tensile strength (S_ut)?

• AModified Mohr (or Coulomb-Mohr) criterion
• BDistortion Energy (von Mises) criterion
• CMaximum Shear Stress (Tresca) criterion
• DJohnson-Cook plasticity model

A notched steel shaft has a geometric stress concentration factor K_t = 2.40. For the given material and notch geometry, the notch sensitivity factor is q = 0.75. What is the fatigue stress concentration factor K_f?

• A2.05
• B1.80
• C2.40
• D1.05

For an X-bar control chart, subgroups of n = 5 shafts give a grand mean of 50.00 mm and an average range R-bar = 0.20 mm. With the control chart constant A2 = 0.577 for n = 5, what are the upper and lower control limits?

• AUCL ≈ 50.115 mm, LCL ≈ 49.885 mm
• BUCL ≈ 50.200 mm, LCL ≈ 49.800 mm
• CUCL ≈ 50.346 mm, LCL ≈ 49.654 mm
• DUCL ≈ 50.058 mm, LCL ≈ 49.942 mm

A machine component made of alloy steel has an ultimate tensile strength S_ut = 800 MPa and an endurance limit S_e = 400 MPa. Under cyclic loading, it experiences an alternating stress amplitude σ_a = 150 MPa and a mean tensile stress σ_m = 200 MPa. Using the Modified Goodman failure criterion, what is the design factor of safety n?

• A1.60
• B2.00
• C1.14
• D2.67

When comparing fatigue failure criteria for ductile metals under fluctuating tensile stresses, why is the Soderberg criterion more conservative than the Goodman criterion?

• ASoderberg anchors the mean stress limit to the yield strength S_y instead of the higher u…
• BSoderberg uses a parabolic curve rather than a linear boundary connecting the stress axes
• CSoderberg divides the alternating endurance limit by an additional empirical safety facto…
• DSoderberg considers both compressive and tensile mean stresses to be equally damaging

In the design of a rotating transmission shaft under steady torsion T and completely reversed bending moment M, which stress components correspond to alternating stress and mean stress according to standard ASME shaft design methodology?

• ABending produces alternating normal stress (σ_a), and steady torsion produces mean shear…
• BBending produces mean normal stress (σ_m), and steady torsion produces alternating shear…
• CBoth bending and steady torsion produce exclusively alternating stresses
• DBoth bending and steady torsion produce exclusively steady mean stresses

A rotating shaft supports two concentrated rotors. Rotor 1 alone causes a static deflection yielding a first critical speed of ω_1 = 120 rad/s, while rotor 2 alone yields ω_2 = 160 rad/s. Using Dunkerley's equation, what is the estimated fundamental critical speed ω_cr of the combined shaft-rotor assembly?

• A96.0 rad/s
• B140.0 rad/s
• C200.0 rad/s
• D68.6 rad/s

A standard full-depth spur gear has a module m = 4 mm and N = 25 teeth. What are the pitch diameter d and the addendum a of this gear?

• APitch diameter d = 100 mm, Addendum a = 4.0 mm
• BPitch diameter d = 100 mm, Addendum a = 5.0 mm
• CPitch diameter d = 6.25 mm, Addendum a = 4.0 mm
• DPitch diameter d = 200 mm, Addendum a = 8.0 mm

A machine shop's monthly fixed costs for a product line are MXN 240,000. Each part sells for MXN 150 and has a variable cost of MXN 90. How many parts per month must be sold to break even?

• A4,000 parts
• B1,600 parts
• C2,667 parts
• D6,000 parts

Why does a helical gear pair generate an axial thrust force on its supporting transmission shaft, whereas a standard spur gear pair does not?

• AHelical gear teeth are inclined at a helix angle ψ relative to the axis of rotation, crea…
• BHelical gears have an elliptical pitch surface that wobbles during rotation
• CHelical gears operate at higher contact ratios, which converts sliding friction into axia…
• DHelical gear tooth addendums are larger than standard spur gear teeth

A deep-groove ball bearing with a basic dynamic load rating C = 32 kN is subjected to a constant equivalent radial load P = 8.0 kN. What is the basic rating life L_10 of this bearing in millions of revolutions?

• A64 million revolutions
• B12 million revolutions
• C101.6 million revolutions
• D4 million revolutions

In the selection of rolling contact bearings under combined radial load F_r and axial thrust load F_a, what is the role of the limiting factor e?

• AIt serves as a threshold: if F_a / F_r ≤ e, thrust is small enough that equivalent dynami…
• BIt defines the mechanical efficiency of the bearing under pure rotational hydrodynamic lu…
• CIt represents the eccentricity ratio of the raceway groove relative to the bearing bore
• DIt specifies the maximum permissible angular shaft misalignment in degrees

A helical compression spring has a spring index C = D/d = 6, wire diameter d = 4 mm, and mean coil diameter D = 24 mm. Under an axial load F = 200 N, what is the maximum torsional shear stress τ_max in the spring wire, taking into account the Wahl curvature correction factor K_w = (4C - 1)/(4C - 4) + 0.615/C?

• A239 MPa
• B191 MPa
• C382 MPa
• D153 MPa

A preloaded bolted joint has a bolt stiffness k_b = 1.0 × 10⁶ N/mm and a clamped member stiffness k_m = 4.0 × 10⁶ N/mm. An initial bolt preload F_i = 20 kN is applied. When an external tensile separating load P = 10 kN acts on the joint, what is the total tensile load F_b experienced by the bolt (assuming joint separation does not occur)?

• A22 kN
• B30 kN
• C28 kN
• D12 kN

In the structural design of an equal-leg fillet weld with leg size h, what is the standard effective throat thickness t used for shear stress calculations?

• At = h · cos(45°) ≈ 0.707 · h
• Bt = h
• Ct = h · sin(60°) ≈ 0.866 · h
• Dt = 0.500 · h

A closed thermodynamic system undergoes a process during which it receives Q = 500 J of heat from the surroundings while performing W = 200 J of boundary work on the surroundings. According to the First Law of Thermodynamics (ΔU = Q - W), what is the change in internal energy ΔU of the system?

• A+300 J
• B+700 J
• C-300 J
• D-700 J

A CNC turning operation has a machine-and-operator rate of MXN 600 per hour, a cycle time of 6.0 minutes per part, and a tooling cost of MXN 5 per part. Setup takes 1.0 hour per batch of 100 parts. What is the manufacturing cost per part?

• AMXN 71.00
• BMXN 65.00
• CMXN 60.00
• DMXN 3,605.00

A reversible Carnot heat engine operates between a high-temperature heat reservoir at T_H = 327°C and a low-temperature sink at T_L = 27°C. What is the maximum theoretical thermal efficiency η_th of this engine?

• A50.0%
• B91.7%
• C8.3%
• DIt cannot be determined without the heat input Q_H

An internal combustion engine modeled on the air-standard Otto cycle has a compression ratio r = 8.0. Assuming air behaves as an ideal gas with a specific heat ratio γ = 1.4, what is the theoretical thermal efficiency η_Otto of the cycle?

• A56.5%
• B44.8%
• C87.5%
• D43.5%

How does an increase in the cutoff ratio r_c (defined as V_3 / V_2, the ratio of cylinder volumes after and before combustion) affect the thermal efficiency of an ideal Diesel cycle at a constant compression ratio r?

• AThe thermal efficiency decreases because heat addition extends later into the expansion s…
• BThe thermal efficiency increases because more fuel energy is injected into the combustion…
• CThe thermal efficiency remains unchanged because efficiency depends strictly on compressi…
• DThe thermal efficiency first doubles and then levels off asymptotically

What sequence of four thermodynamic processes comprises the ideal simple Rankine vapor power cycle?

• AIsentropic pumping, constant-pressure heat addition in boiler, isentropic expansion in tu…
• BIsothermal compression in pump, constant-volume combustion, isentropic expansion in turbi…
• CIsentropic compression, isothermal heat addition, isentropic expansion, isothermal heat r…
• DPolytropic pumping, constant-volume heating, isentropic expansion, constant-volume cooling

In modern utility steam power plants operating on a modified Rankine cycle, what is the primary operational advantage of introducing steam reheat between the high-pressure and low-pressure turbine stages?

• AIt prevents excessive moisture content at the low-pressure turbine exhaust, protecting bl…
• BIt eliminates the need for a condenser by discharging exhaust steam directly to atmosphere
• CIt reduces boiler operating pressure down to atmospheric levels
• DIt cools the feed pump to prevent cavitation

In an ideal air-standard Brayton cycle with fixed minimum inlet temperature T_1 and fixed maximum turbine inlet temperature T_3, how does the net work output behave as the compressor pressure ratio r_p is varied from 1 to its thermodynamic maximum?

• ANet work is zero at r_p = 1, reaches a maximum at an intermediate optimum pressure ratio,…
• BNet work increases monotonically with pressure ratio without bound
• CNet work decreases continuously from a peak at r_p = 1 down to zero
• DNet work remains completely constant regardless of pressure ratio

A standard vapor-compression refrigeration unit operates with an evaporator heat absorption rate q_L = 150 kJ/kg of refrigerant. The compressor requires an isentropic work input w_in = 30 kJ/kg. What is the Coefficient of Performance (COP_R) of this refrigeration system?

• A5.0
• B0.20
• C6.0
• D4.0

A vertical rectangular floodgate of height h and width b is submerged in water such that its top edge is flush with the free water surface. At what vertical depth below the water surface does the resultant hydrostatic force act (center of pressure y_p)?

• A2/3 · h
• B1/2 · h
• C3/4 · h
• D1/3 · h

Which set of physical assumptions is required for the classical Bernoulli equation (p/ρg + V²/2g + z = constant) to hold strictly between two points in a fluid flow?

• ASteady flow, incompressible fluid, inviscid (frictionless) flow, along a single streamlin…
• BUnsteady flow, compressible gas, highly viscous fluid, turbulent boundary layer
• CSteady flow, ideal gas, adiabatic flow with major shock waves
• DIsothermal flow, high Mach number, rotational vortex flow across streamlines

Water flows through a horizontal circular pipe that tapers from an internal diameter D_1 = 200 mm to D_2 = 100 mm. If the average flow velocity at section 1 is V_1 = 2.0 m/s, what is the average flow velocity V_2 at section 2?

• A8.0 m/s
• B4.0 m/s
• C1.0 m/s
• D16.0 m/s

For fully developed laminar flow of a Newtonian fluid inside a smooth circular pipe (Reynolds number Re < 2300), how is the Darcy friction factor f related to the Reynolds number?

• Af = 64 / Re
• Bf = 16 / Re
• Cf = 0.316 / Re^0.25
• Df = 0.079 / Re^0.25

A CNC lathe is purchased for MXN 1,200,000. It is expected to last 10 years and to have a salvage value of MXN 200,000. Using straight-line depreciation, what is the annual depreciation charge that should be included in the machine-hour rate?

• AMXN 100,000 per year
• BMXN 120,000 per year
• CMXN 140,000 per year
• DMXN 20,000 per year

On the Moody chart, in the 'wholly rough turbulent' regime at very high Reynolds numbers, what parameter governs the value of the Darcy friction factor f?

• AThe relative roughness (ε / D) alone, becoming independent of Reynolds number
• BThe Reynolds number (Re) alone, becoming independent of pipe surface roughness
• CThe fluid viscosity and velocity profile alone
• DThe pipe length to diameter ratio (L / D)

A centrifugal pump delivers water (density ρ = 1,000 kg/m³, g = 9.81 m/s²) at a volumetric flow rate Q = 0.050 m³/s against a total dynamic head H = 40.0 m. What is the theoretical hydraulic power P_h imparted to the fluid?

• A19.6 kW
• B15.7 kW
• C24.5 kW
• D2.0 kW

How is the steady-state operating point of a centrifugal pumping system graphically determined on a head-versus-flow rate (H-Q) diagram?

• ABy the point of intersection between the pump head-capacity curve and the system head cur…
• BBy the point of maximum pump mechanical efficiency on the efficiency curve
• CBy the point of maximum shut-off head at zero flow rate
• DBy the point where static elevation head equals velocity head

A centrifugal pump operating at an impeller speed of N_1 = 1,750 rpm draws a shaft power of P_1 = 10 kW. If a variable frequency drive increases the pump speed to N_2 = 3,500 rpm (doubling the speed) while maintaining geometric similarity, what is the new required shaft power P_2 according to the pump affinity laws?

• A80 kW
• B40 kW
• C20 kW
• D160 kW

To prevent destructive cavitation in a centrifugal pump installation, what fundamental hydraulic condition must be satisfied regarding Net Positive Suction Head (NPSH)?

• ANPSHA > NPSHR (available NPSH must exceed required NPSH by a safe margin)
• BNPSHA < NPSHR
• CNPSHA must equal zero gauge pressure
• DNPSHR must exceed atmospheric pressure head

In a two-stage reciprocating gas compressor operating between suction pressure P_1 and final discharge pressure P_2 with perfect intercooling between stages back to inlet temperature T_1, which intermediate pressure P_i minimizes the total required compression work?

• AP_i = √(P_1 · P_2)
• BP_i = (P_1 + P_2) / 2
• CP_i = P_2 - P_1
• DP_i = (P_1 · P_2) / (P_1 + P_2)

A plane furnace wall consists of a material with thermal conductivity k = 0.80 W/(m·K), thickness L = 0.20 m, and surface area A = 5.0 m². Under steady one-dimensional conditions, the inner surface is at T_1 = 600°C and the outer surface is at T_2 = 100°C. What is the conductive heat transfer rate q through the wall?

• A10.0 kW
• B2.0 kW
• C15.6 kW
• D0.40 kW

A quality team records the causes of 200 rejected castings: porosity 90, misruns 50, sand inclusions 30, cold shuts 20, and other causes 10. Which quality tool presents these causes in descending order of frequency with a cumulative percentage line, so that the 'vital few' causes can be attacked first?

• APareto chart
• BCause-and-effect (Ishikawa) diagram
• CX-bar and R control chart
• DScatter diagram

A small diffuse-gray body with surface area A, emissivity ε, and absolute temperature T_1 is completely enclosed by large isothermal surroundings at absolute temperature T_2. Using the Stefan-Boltzmann constant σ, what is the net radiative heat exchange rate q_rad?

• Aq_rad = ε · σ · A · (T_1⁴ - T_2⁴)
• Bq_rad = ε · σ · A · (T_1 - T_2)⁴
• Cq_rad = σ · A · (T_1⁴ - T_2⁴) / ε
• Dq_rad = ε · σ · (T_1⁴ - T_2⁴) / A