TENSION MEMBERS
• Tension members are among the most basic of structural
elements
• These are axially loaded members stressed in tension and are
used in steel structures in various forms
• Can be found in:
• Bracing system
• Trusses
• BASIC MODES OF FAILURE
• Tensile Yielding
• Occurs when the stress in the gross area of the section is large
enough to cause excessive deformation.
• Tensile Rupture
• Occurs when the stress on the effective area of the section is large
enough to cause the member to fracture, which usually occurs across a
line of bolts where the tension member is weakest.
• G ROSS SECTIO N YIELDING
LRFD ∅𝑃𝑛 = ∅𝐹𝑦𝐴𝑔
ASD
where:
𝐹𝑦𝐴𝑔
𝑃𝑛
=
Ω𝑡
Ω𝑡
• ∅ = resistance factor
• ∅ = 0.90
• Ω = 1.67
𝐹𝑦
= minimum
yield stress
𝐴𝑔 = gross area of the tension member
∅𝑃𝑛 = design capacity
• NET SECTION FRACTURE
LRFD ∅𝑃𝑛 = ∅𝐹𝑢𝐴𝑒
ASD
Where
𝑃𝑛
Ω𝑡
=
𝐹𝑢𝐴𝑒
Ω
𝑡
∅ = resistance factor
• ∅ = 0.75
• Ω = 2.00
• 𝐹𝑢 = minimum tensile stress
• 𝐴𝑒 = effective area of the tension member
• ∅𝑃𝑛= design capacity
• EFFECTIVE NET AREA
𝐴𝑒 = 𝐴 𝑛 𝑈
where:
• A𝑒 - effective net area
• 𝐴 𝑛 - net area of the tension member
• U - shear lag factor
• GROSS AREA AND NET AREA
• Tension member that is connected by welds, the net area equals
the gross area
• Net area of a tension member with fasteners that are in is the
difference between the gross cross-sectional area and the area of
the bolt holes
𝐴𝑛 = 𝐴𝑔 − 𝐴h𝑜𝑙𝑒𝑠
Where:
• 𝐴h𝑜𝑙𝑒𝑠 = 𝑛 (d𝑏
+ 1/8) t
• GROSS AREA AND NET AREA
• Tension members with a series of holes in a diagonal or zigzag pattern,
which might be used when bolt spacing is limited there may exist several
possible planes of failure that need to be investigated.
• For a failure plane where one or more of the failure planes is at an angle
𝐴𝑛 = 𝐴𝑔 − ∑ 𝑑𝑕 𝑡 + ∑
𝑡
4𝑔
• Where
s - Longitudinal center-to-center spacing or pitch between two consecutive
holes
g - Transverse center-to-center spacing or gage between two consecutive
holes
• Example 1:
• Calculate the net area of the plate shown connected with 3/4” diameter bolts
• Example 2:
• Calculate the net area of a rolled shape W10 x 49 steel connected with 3/4”
diameter bolts (refer to Table 1-1 page 1-26 AISC - SCM)
• STAGGERED BOLT CONNECTION
• Example 1:
• Calculate the net area of the plate shown connected with ¾ ” diameter bolts.
• STAGGERED BOLT CONNECTION
• Example 2
• Compute 𝐴 𝑛 and 𝐴𝑒 for a 14-in.-wide and 1/2-in. thick plate subject to tensile loading
with staggered holes as shown.