Practice Problems ME 3201: Machine Design
Fall 2023
Chapter 03: Load & Stress Analysis
1. A carbon steel ball is pressed against a flat plate of same material with a force of 50 N. Find the minimum
diameter of the steel ball if. Also determine the magnitude and location of maximum shear stress in the ball.
2. An aluminum alloy cylindrical roller with diameter 40 mm and length 40 mm rolls on the inside of a cast iron
ring having an inside radius of 100 mm, which is 40 mm thick. Find the maximum contact force if the
maximum shear stress is not to exceed 40 MPa.
3. Two cylindrical parts are to be assembled to make an interference fit. The nominal diameter of the assemble
is 100 mm. Before assembly, the inner member (copper) has an outer radius that is 0.2 mm larger than the
inner radius of the outer member (aluminum).
If there is no force acting on the assembly, determine the maximum and minimum principal stress in both
members. Assume Poisson’s ratio of 0.3 for both the materials. Also take ri =30 mm for copper and ro = 80
mm for aluminum cylinder.
4 A 20 mm diameter roller is in contact with a plate-cam surface whose width is 12 mm and the radius of
curvature of the cam surface is 85 mm. If the Hertz compressive stress is not to exceed 2000 MPa, determine
the maximum load that can be applied.
If the follower has the plane flat surface keeping other parameter same as above, then determine the maximum
load that can be applied.
Chapter 04: Deflection & Stiffness
1. A cantilever beam of Length L, Elastic modulus E, Area moment of inertia I is subjected to a concentrated
load P at the free end of the beam. Determine the expression for the deflection at that point using Castigliano’s
theorem.
2. A simply supported beam of Length L, Elastic modulus E, Area moment of inertia I is subjected to a
concentrated load P at the mid-point. Determine the expression for the deflection at that point using
Castigliano’s theorem.
Chapter 07: Shafts & Shaft Components
1. For a Force fit with 35 mm Basic size, Find the followings:
(a) Hole and Shaft dimensions
(b) Lower and Upper deviation of shaft
(c) Diametral Interference
2. For a Close Running fit with 35 mm Basic size, Find the followings:
(a) Hole and Shaft dimensions
(b) Lower and Upper deviation of shaft
(c) Diametral Clearence
3. For a 400mm H7/k6 fit, Find the followings:
(a) Hole and Shaft dimensions
(b) Lower and Upper deviation of shaft
(c) Diametral Clearence
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Practice Problems ME 3201: Machine Design
Fall 2023
Chapter 08: Screw, Fasteners & Design of non-permanent joints
1. A triple threaded steel bolt (M20, coarse-pitch, property class 12.9) connects two identical elastic plates. After
snug fit, the nut is turned th of a full rotation. Resulting clamping force on plate is 80 KN while the bolt
elongates by 0.70 mm.
(a) Calculate stiffness of the bolt and members, and the joint constant
(b) Determine the external force that will cause the join of separation of this assemble.
(c) Examine if the material will fail at the separation or not.
2. A square thread power screw is to carry a load of 3 KN. The screw is double threaded, has 4 mm pitch, 32 mm
pitch diameter and mean diameter and 80 mm collar diameter.
(a) Calculate the minimum value of friction coefficient if the screw must be self-locked in the absence of
collar friction.
(b) Assume that friction coefficient is present in all surfaces of contact. Determine the torque and mechanical
advantage if the load must be raised in absence of collar friction.
(c) Find the torque required to overcome collar friction when the load is lowered.
3. An ACME thread (2α=29°) power screw carries a load of 2.5 KN. The screw is single threaded that has a 6
mm pitch, 30 mm pitch diameter & mean diameter, 80 mm collar diameter and the friction coefficient is 0.05.
(a) Determine if the screw is self-locked in the absence of collar friction.
(b) Find the torque and mechanical advantage if the load is lifted in the absence of collar friction.
(c) Net torque required to lift the load if collar friction is present.
Chapter 09: Welding, Bonding & Design of permanent joints
1. A steel bar of 5 mm thickness, to be used as a beam, is welded to a vertical support by two fillet welds as
shown in the figure. (b=50 mm, c=150mm, d=50mm)
(a) Find the safe bending force F if the allowable shear stress in the welds is 140 MPa.
(b) Determine the allowable load if the electrode is E7010, the bar is hot-rolled 1020, and the support is hot-
rolled 1015.
2. A steel bar of 5 mm thickness, to be used as a beam, is welded to a vertical support by two fillet welds as
shown in the figure. (b=50 mm, c=150mm, d=30mm)
(a) Find the safe bending force F if the allowable shear stress in the welds is 140 MPa.
(b) Determine the allowable load if the electrode is E7010, the bar is hot-rolled 1020, and the support is hot-
rolled 1015.
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Practice Problems ME 3201: Machine Design
Fall 2023
Chapter 19: Finite Element Analysis
1.
Metal A
P1 Metal B P2
1.52 m 3.05 m
Cross sectional area of metal A and B is12.9 cm 2 and 8.06 cm2. Modulus of elasticity of metal A and B is
6.9×109 N/m2 and 3.5×1010 N/m2. External force P1 and P2 are 4.45 KN and 2.23 KN respectively.
Determine the followings using a minimum number of elements:
(a) Nodal displacements
(b) Element stresses
(c) Support reaction
(d) Element forces
2.
Aluminum P Steel
300 mm 400 mm
For Aluminum bar: A1=2400 mm2, E1=0.7×105 MPa, α1=22×10-6 /℃
For Steel bar: A2=1200 mm2, E2=2×105 MPa, α2=12×10-6 /℃
Determine the followings using Finite Element method due to applied force P = 400 kN and temperature rise
of 30℃:
(a) Nodal displacements
(b) Element stresses
(c) Support reaction
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