Design of Tension Members
Tension members are linear members in which axial forces act so as to elongate (stretch) the member. A rope, for example, is a tension member. Tension members carry loads most efficiently, since the entire cross section is subjected to uniform stress. Unlike compression members, they do not fail by buckling.
Behavior of Tension Members
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| Load – Elongation of Tension Members |
since axially loaded tension members are subjected to uniform tensile stress, their load deformation behaviour is similar to the corresponding basic material stress strain behaviour. Mild steel members exhibit an elastic range (a-b) ending at yielding (b). This is followed by yield plateau (b-c). In the Yield Plateau the load remains constant as the elongation increases to nearly ten times the yield strain. Under further stretching the material shows a smaller increase in tension with elongation (c-d), compared to the elastic range. This range is referred to as the strain hardening range. After reaching the ultimate load (d), the loading decreases as the elongation increases (de) until rupture (e). High strength steel tension members do not exhibit a well-defined yield point and a yield plateau. The 0.2% offset load, T, as shown in figure usually taken as the yield point in such cases.
Concentrically Loaded Tension members
- Members without holes - Although steel tension members can sustain loads up to the ultimate load without failure, the elongation of the members at this load would be nearly 10-15% of the original length and the structure supported by the member would become un-serviceable. Hence, in the design of tension members, the yield load is usually taken as the limiting load.
Ny = An* fy
where, An is net area
fy is yield strength of material used
- Members with holes - the presence of small local holes in a tension member causes early yielding around the holes. This means that area around the holes reaches yielding, while the rest of cross section is below yield stress. The average stress around the hole is about 3 times the average stress in the net area. As small length of member (in red) adjacent to the holes reaches ultimate load before the rest of the part. Since only this length ( in red) would stretch a lot at the ultimate stress, and the overall member elongation need not be large, as long as the stresses in the gross section is below the yield stress. Hence Ultimate load is taken as limiting load.
In statically loaded tension members with a hole, the point adjacent to the hole reaches yield stress, fy , first. On further loading, the stress at that point remains constant at the yield stress and the section plastifies progressively away from the hole (b), until the entire net section at the hole reaches the yield stress, fy , (c). Finally, the rupture (tension failure) of the member occurs when the entire net cross section reaches the ultimate stress, fu.
The fracture load for members with significant holes is ,
Nu = An *fu
where An is the net cross sectional area is perpendicular to the line of
action of the load, and is given by
An = Ag - Σ d*t
where d is the diameter of a hole, t the thickness of the member at the hole, and the summation is carried out for all holes in the cross-section under consideration. Nu is determined by the weakest cross-section, and therefore by the minimum net area An.
A member which fails by fracture before the gross yield load can be reached is not ductile, and there is little warning of failure.
In many practical tension members with more than one row of holes, the reduction in the
cross-sectional area may be reduced by staggering the rows of holes (see figure below). In this case, the possibility must be considered of failure along a zig-zag path such as ABCDE in the figure, instead of across the section perpendicular to the load.
Picture
The minimum amount of stagger Spm for which a hole no longer reduces the area of the member depends on the diameter 'd' of the hole and the inclination Sg/sp of the failure path, where Sg is the gauge distance between the rows of holes. An approximate expression for this minimum stagger is:
Spm = (4*Sg*d)^0.5
When the actual stagger sp is less than spm, some reduced part of the hole area Ah must be deducted from the member area A , and this can be approximated by ,
Ah = d*t( 1- Sp^2/4*sg*d)
An = Ag - Σ d*t + Ah
Net area has increased because cross sectional length of BC is greater than what it would have been if BC was perpendicular to direction of application of force.
Design According to Australian Standards
According to AS4100, the tensile force N* must satisfy the inequality,
N* <= ϕ Nt
where, ϕ is capacity reduction factor ϕ = 0.9
Nt is nominal section capacity.
Nt is lesser of:
Nt = Ag*fy [limit state of yielding ]
Nt = 0.85*Kt *An*fu [ limit state of fracture of net cross sectional area]
References
- Trahair, N. S and M. A Bradford. The Behavior And Design Of Steel Structures To AS 4100. London: E & FN Spon, 1998. Print.
- Salmon, Charles G and John Edwin Johnson. Steel Structures. New York: Harper & Row, 1980. Print.
- "DESIGN OF TENSION MEMBERS". http://www.steel-insdag.org/. Web. 25 July 2016.
- "NPTEL :: Civil Engineering - Design Of Steel Structures I". Nptel.ac.in. N.p., 2016. Web. 25 July 2016.
