23
en
= Cross sectional area of the bolt
= Modulus of elasticity (Young’s Modulus)
The cross sectional area of the bolt is defined as the average area of a fastener under stress. This factor is
only used by the gauge in the calculation of load. It has no effect on stress or elongation, time, or strain, and
is directly proportional to the load measured ultrasonically. If the cross sectional area is in error by 5%, the
load measurement will also be in error by 5% proportionally. For a cylindrical bolt with the same geometry,
the area may be approximated as follows:
where:
= Area
= Minor diameter of the bolt allowing for threads
For bolts with complex geometry, the areas should be estimated by averaging each individual area and
length. In the case of a hollow fastener, the area of the hole must be subtracted from the overall area. The
area of a fastener with complex geometry can be estimated as follows:
where:
= Area of a region
= Length of a region
The value for the Modulus of Elasticity (E), should be provided directly from the manufacturer of the bolts.
The effective length is the average length of the fastener under stress when a load is applied. For an applied
constant load, the elongation of a fastener is directly proportional to the effective length. Therefore, errors
in the effective length will result in load errors by a proportional amount. The effective length of a fastener
is a combination of the actual clamp length of the joint being fastened, plus that area of stress found in the
head, nut(s), and or blind hole of the fastener - see examples which follow.
A
E
A
π
D
2
----
⎝ ⎠
⎛ ⎞
2
=
A
D
A
AVG
AL
∑
L
∑
---------------
=
A
L
