Design the input shaft using the following procedure:


Step # 1 - Determine the conceptual shape/design of the shaft

  1. Draft a rough sketch (top view) of the shaft
  2. Determine the lengths of the various sections of the shaft by:
    1. Considering the face width of the pinion and/or the gear
    2. Considering approximate hub widths the gears
    3. Considering values for the air gaps
    4. Considering a width of the bearings that may be used
  3. Determine the distances between all the load/reaction locations
  4. Assume that both shafts lie on the same horizontal plane


Step # 2 - Select Material for the Shaft

Assume the basic shaft diameters and make a first trial material selection for the shaft

Hint: For strength based designs, shafts having diameters less than 3.5" are usually made from a cold drawn steel in order to resist fatigue


For D 3.5" Cold Drawn (CD) Material - better surface finish and easily machinable

For D 3.5" Hot Rolled (HR) or preferably Quenched & Treated (Q&T) - generally rough surface but low cost


Step # 3 - Select safety factors for the design of each shaft

Basic Rules:

Safety Factor



For ductile materials where a high level of confidence exists in the loads, material properties and operating conditions


For brittle materials where a high level of confidence exists and operating conditions are well known


For ductile materials with some doubt about the adequacy of material properties data, loads or the stress analysis


For uncertain conditions about same combination of material properties, loads and the stress analysis



Step # 4 - Calculate the torque and sketch torque diagram for the shaft

Using the following equation, calculate the torque of each shaft:


P is power in HP

n is speed in rpm

Draw the torque diagram based upon the torque value(s)


Step # 5 - Determine the tangential and normal forces on each of the gears

Tangential Force:

Wt = T/(d/2) where d is the gear’s pitch diameter

Radial Force:

Wr = Wt (Tan F )

Where: F (Pressure angle) is 20

T is torque

D is gear pitch diameter


Step # 6 - Perform a complete force analysis (x & y-direction) for the shaft and draw force diagrams showing all forces acting on the shaft and compute the bearing reactions at the bearing seat locations and select bearings

Resultant reaction at any point is given by:


Step # 7 - Draw shear force and bending moment diagrams for the shafts, both in the vertical and horizontal planes and draw the resultant bending moment diagrams

 Do the following for the shaft:

  1. Draw SFD & BMD in the vertical direction (y-axis)
  2. Draw SFD & BMD in the horizontal direction (z-axis)
  3. Draw RBMD on graph paper, to scale with a sketch of the shaft at the top


Step # 8 - Determine the basic shaft diameters using static analyses and rough assumptions

Do the following for the shaft:

  1. Using the torque and RBMD diagrams, perform static analyses to determine the static diameters of the different sections of the shaft
  2. Where static analyses are not possible or are unnecessary, assume diameters based upon the diameters of the adjacent sections


Step # 9 - Determine the shaft diameters using fatigue analyses

Do the following for the shaft:

  1. Determine critical points by first identifying the stress concentration locations
  2. Perform fatigue analyses at each critical (fatigue) location to determine the fatigue diameters of the shaft
  3. Summarize the preliminary shaft diameters from the static and fatigue analyses