Bolt Stretching Case Study
Introduction
A bolt and nut are designed to act together as the internal threaded fastener (nut) is tightened onto the
externally threaded fastener (bolt). The bolt is forced to stretch and elongate. This stretching/elongation
is maintained by the head of the bolt and the nut on the joint thereby maintaining the joint at the
desired tension (Bolt tensioning).
As a rule, the joint will have been designed with sufficient fastener to apply the required clamp load at
65% of the fastener proof load stress figure i.e. well below the fastener’s yield point.
Yield point or yield strength
It is defined as the load that is necessary to stretch the fastener to the point where, after the load is
removed, the bolt will not return to its original or previous length. It has moved from being elastic to
plastic behaviour.
In order for the fastener to incur a longer length part of bolt donates material. This will come from the
threads, which are the weakest part of the bolt. A section of the threaded portion of the bolt wall
suffers a reduction of area and will “neck out”, creating a “dog bone” appearance. The change in stress
area makes the bolt considerably weaker and as the bolt is stretched even further the clamping load
decreases. Additional stretching (caused by operator attempting to retighten the joint and fastener) will
cause the bolt to break at its tensile point.
Tensile strength
It is the maximum tension applied – load a fastener can support i.e. how far it will stretch prior to failure
or coincident with its fracture.
Proof load stress
The tensile load applied to a fastener, which causes the material to exceed its plastic limit.
Fasteners are generally “torqued” to 65% of the designated proof load stress figure for that fasteners
specific diameter and thread form (Bolt tensioning). However other sources suggested as high as 80%
Preload
Bolts are often tightened by applying torque to the head or nut, which causes the bolt to stretch. The stretching results in bolt tension or preload, which is the force that holds a joint together. Torque is relatively easy to measure with a torque wrench, so it is the most frequently used indicator of bolt tension. Unfortunately, a torque wrench does not measure bolt tension accurately, mainly because it does not take friction into account. The friction depends on bolt, nut, and washer material, surface smoothness, machining accuracy, degree of lubrication, and the number of times a bolt has been
installed. Fastener manufacturers often provide information for determining torque
requirements for tightening various bolts, accounting for friction and other effects. If this information is not available, the methods described in what follows give general guidelines for determining how much tension should be present in a bolt, and how much torque may need to be applied to arrive at that tension.
High preload tension helps keep bolts tight, increases joint strength, creates friction between parts to resist shear, and improves the fatigue resistance of bolted connections
.
The recommended preload Fi, which can be used for either static (stationary) or fatigue (alternating) applications, can be determined from:
Fi = 0.75 × As × 𝜎p for reusable connections,
and Fi = 0.9 × As × 𝜎p for permanent connections.
where :F i is the bolt preload,
As is the tensile stress area of the bolt,
𝜎p is the proof strength of the bolt.
value of proof strength can be obtained from:
𝜎y is the yield
𝜎p = 0.85 × 𝜎y,
where 𝜎y is the yield
strength of the material. Soft materials should not be used for threaded fasteners. Once the required preload has been determined, one of the best ways to be sure that a bolt is properly tensioned is to measure its tension directly with a strain gage. Next best is to measure the change in length (elongation) of the bolt during tightening, using a micrometer or dial indicator. Each of the following two formulas calculates the required change in length of a bolt needed to make the bolt tension equal to the recommended preload. The change in length δ of the bolt is given by:
If measuring bolt elongation is not possible, the torque necessary to tighten the bolt must be estimated. If the recommended preload is known, use the following general relation for the torque: T = K × Fi × d,
where T is the wrench torque,
K is a constant that depends on the bolt material and size,
F is the preload,
d is the nominal bolt diameter. A value of K = 0.2 may be used in this equation for mild-steel bolts in the size range of 1⁄4 to 1 inch. Forother steel bolts, use the following values of K: nonplated black finish, 0.3; zinc-plated,
0.2; lubricated, 0.18; cadmium-plated, 0.16. Check with bolt manufacturers and suppliers
for values of K to use with bolts of other sizes and materials
The proper torque to use for tightening bolts in sizes up to about 1⁄2 inch may also be determined
by trial. Test a bolt by measuring the amount of torque required to fracture it (use bolt, nut, and washers equivalent to those chosen for the real application). Then, use a tightening torque of about 50 to 60 per cent of the fracture torque determined by the test.
The tension in a bolt tightened using this procedure will be about 60 to 70 per cent of the
elastic limit (yield strength) of the bolt material.
The table that follows can be used to get a rough idea of the torque necessary to properly
tension a bolt by using the bolt diameter d and the coefficients b and m from the table; the
approximate tightening torque T in ft-lb for the listed fasteners is obtained by solving the
equation
Bolt stretching according Hooke's Law
Elongation
Bolt stretching according Hook's Law can be expressed as
𝛿 = F L / E A (1)
where
𝛿 = change in length of bolt (inches, mm)
F = applied tensile load (lb, N)
L = effective length of bolt where tensile strength is applied (inches, m)
E = Young's Modulus of Elasticity (psi, N/m²)
A = tensile stress area of the bolt (square inches, m²)
Stress Area
UN and UNR Bolts Tensile Stress Area
The tensile stress area can be expressed as
A = 0.7854 (d - 0.9743 / n)² (2)
where
d = nominal diameter of bolt (inches, m)
n = number of threads per inch (pitch)
ISO 898 Bolts Tensile Stress Area
Tensile stress area in bolts according ISO 898-1 Mechanical properties of fasteners made of carbon steel and alloy steel:
As,nom = (π / 4) ((d2 + d3)/ 2)²
where
(As,nom = nominal stress area (m, mm²
d2 = the basic pitch diameter of the external thread according ISO 724 ISO general-purpose metric screw threads -- Basic dimensions (m, mm
(d3 = d1 - H / 6 = the minor diameter of external tread (m, mm
d1 = the basic minor diameter of external thread according ISO 724
H = the height of the fundamental triangle of the thread according ISO 68-1 ISO general purpose screw threads (m, mm
Tensile Stress
Tensile stress can be calculated as
σ = F / A (3)
where
σ = tensile stress (psi, N/m² (Pa))
Example - Bolt Stretching - Imperial Units
stud diameter : 7/8 inches
thread pitch : 9
Young's Modulus steel : 30 106 psi
designed bolt load : 10000 lb
effective length : 5 inches
The tensile stress area can be calculated as
A = 0.7854 ((7/8 in) - 0.9743 / 9)²
= 0.46 (in²)
The elongation can be calculated as
dl = (10000 lb) (5 in) / ((30. 10⁶ psi) (0.46 in²))
= 0.0036 (inches)
The tensile stress can be calculated as
σ = (10000 lb) / (0.46 in²)
= 21740 psi
Related ISO Standards
ISO 68:1973 ISO general purpose screw threads - Basic profile
ISO 261:1973 ISO general purpose metric screw threads - General plan
ISO 262:1973 ISO general purpose metric screw threads - Selected sizes for screws, bolts and nuts
ISO 724:1993 ISO general-purpose metric screw threads - Basic dimensions
ISO 965-1:1980 ISO general purpose metric screw threads - Tolerances - Part 1: Principles and basic data
ISO 965-2:1980 ISO general purpose metric screw threads - Tolerances - Part 2: Limits of sizes for general purpose bolt and nut threads - Medium quality
ISO 965-3:1980 ISO general purpose metric screw threads - Tolerances - Part 3: Deviations for constructional threads
ISO 1502:1996 ISO general-purpose metric screw threads - Gauges and gauging
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