Quiz #4 – ME 314

Check bolt size when used for clamping plates with cyclic loading

  1. A 1 in UNC bolt of Grade 5 with fatigue resisting rolled threads is clamping a pair of plate. The external load varies from 0 to 10000 lbs. The initial tension is 75% of the proof load. Routine calculations show that Km = 5 Kb. Find the factor of safety guarding against fatigue failure.

a)Calculate the bolt initial tension: ______

b)Calculate the bolt’s minimum tension:______

c)Calculate The bolt’s maximum tension:______

d)Calculate the bolt’s minimum nominal stress (nominal: Force /Area)______

e)Calculate the bolt’s maximum nominal stress:______

f)In this fatigue analysis should we apply the stress concentration factor: (Yes No)

g)Calculate the bolt’s mean stress:______

h)Calculate the bolt’s alternating stress amplitude:______

i)Look up the endurance limit of this bolt:______

j)Look up the tensile strength of this bolt:______

k)Draw the Modified Goodman diagram for this bolt (not to scale)

l)Locate the point corresponding to the initial tension (without application of the external load) on the diagram. Label it as point A

m)Draw a line from this point (initial tension) that shows how the mean and alternating stresses increase as the external load goes from zero to maximum. This is called the load line.

n)Locate the point corresponding to the calculated mean and alternating stresses – this is called the load point. Label it as point B.

o)Label the point of intersection of the load line with Goodman diagram line as point C. This point corresponds to the locating that leads to the eventual failure of the bolt.

p)The ratio AC/AB is the margin of safety against fatigue failure. The formula is EQ 8-38. Using this formula calculate the factor of safety:______

  1. One way to increase fatigue resistance is to select smaller screws that lead to a smaller joint index C (True False)
  1. Another way of increasing fatigue resistance is to decrease the initial tension (True False).

Design of bolts for brackets under shear

A bracket is bolted to a wall using four screws in a 2 by 2 inch square pattern. A load of 1000 lbsis applied to the hole in the bracket (not shown). The bolts are ½ in UNC – 13 and Grade-2. We want to determine the factor of safety guarding against bolt shank yielding.

Analysis Assumptions:

  • The bracket is rigid
  • All screws have the same fit to the screw holes
  • The friction is lost – no load carried by the wall friction
  • The shear force in a screw is proportional to its distance to the centroid of the pattern of screws.
  • The shear load is taken by the screw shanks
  1. Statics problem. Move the applied load on the plate to where the centroid of the pattern of screws is located – show the resulting forces and force moments.
  2. Calculate the reaction shear force in each screw as a result of to the direct shear force alone:______
  3. Calculate the reaction shear in each screw as a result of to the torsional shear moment alone:______
  4. Combine the shear forces in (5) and (6) for the screw with highest shear load to obtain the resultant shear force in the screw: ______
  5. Calculate the shear stress in the screw shank:______. Look up the yield strength of the screw:______. Determine the factor of safety :______

If the bracket had a triangular patter of screws as shown, which screw sees the most load? (A B C)