In this article we will discuss about:- 1. Introduction to Tension Members in Structural Frame 2. General Considerations of a Tension Member 3. Slenderness Ratio 4. Block Shear Failure and Shear Drag 5. Failure Modes 6. Design Strength 7. Factors Affecting the Design 8. Positioning of Bolts

#### Introduction to Tension Members in Structural Frame:

A tension member is a member which transmits a direct axial pull between two points in a structural frame. A rope supporting a load or a cable in a suspension bridge is an obvious example of a tension member. There are however a few cases in which a member which is basically a tension member, may, also be subjected to a bending moment either due to the eccentricity of the longitudinal load or due to transverse loads acting in addition to the main longitudinal load.

A tension member may have bolted or welded end connections. The effective sectional area of a tension member is less than its gross-sectional area due to bolt holes. A tension member has its unique property that it does not buckle. A tension member undergoes elongation and can extend until it reaches its ultimate strength. As the tensile load reaches the ultimate load the member reaches a failure state. A member in tension can reach a failure state due to excessive elongation or by rupture of its section.

The analysis of a member subjected to tension is probably the most straight forward to all structural analysis. The design of a tension member essentially consists of ensuring that the provided cross sectional area is at least sufficient to resist the tensile load applied. The manner of jointing the member to other parts will influence the manner in which the tensile force is transferred into the member.

In the case of fastening by bolts, the presence of holes in the section of the member has a direct effect on the strength of the member. We consider this problem by knowing its gross and net sectional area. The gross area refers to the original cross-sectional area of the member and the net area refers to the reduced sectional area after deductions due to the presence of bolt holes.

In a tension member the effect of a hole amounts to absence of some material and hence amounts to loss of strength. It may also be realized that in the immediate vicinity of a boll hole stress concentrations will occur and the same will also be affected by the force applied by the bolt. However since steel is ductile, it is usual to neglect these effects and to determine the net sectional area simply by deducting the area of the bolt holes from the gross-sectional area.

While making such deductions it should be noted that most of the types of bolts are provided in clearance holes, the diameter of the hole being made slightly larger than the bolt diameter. The diameter of bolt hole is usually 2 mm larger than that of a bolt for bolt diameters up to 24 mm. The absence of some material at sections where bolt holes exist, one may expect that the member may fail at the smallest net section, i.e., across a line of holes.

However since it is desirable that a failure occurs as a ductile failure rather than as a brittle failure at collapse state. From this point of view it is desirable to ensure that the gross-section yields before the net section reaches the ultimate stress.

To reach this condition it is desirable to ensure that the ratio of the net area to the gross area of the section exceeds the ratio of yield strength to the ultimate strength. Such planning greatly increases the extent of extension the member can sustain and therefore offers a surer indication of the impending failure.

In structures of buildings and bridges, tension members occur in various ways like-(i)Tension chords and internal ties of trusses, (ii)Tension braces, (iii) Hangers supporting floor beams, (iv) Guy wires to towers, (v) Deck suspenders of suspension bridges and (vi) Tie rods connecting purlins.

Tension members may occur as minor tension members such as bars, flats etc., or as major tension members of roof trusses and bridge trusses.

A cable is a flexural member available in various types for use in cable supported bridges. The form of a cable depends upon how it is made up.

A wire is a single continuous length of metal drawn from a cold rod.

A prestressing wire is a high tension steel wire used in prestressed concrete members.

A structural strand consists of wires helically coiled about a central wire to form a symmetrical section.

A parallel wire stand consists of individual wires arranged in a parallel configuration, without providing the helical twist.

A structural rope consists of a number of strands helically wound around a core which consists of either a strand or another rope.

It is usual to galvanize the individual wires in a strand to provide resistance to corrosion. In addition the finished cable is subjected to prestretching for a sufficient interval of time to remove any structural deformation which might have been caused by radial and axial adjustment of the wires or strands.

#### General Considerations of a Tension Member:

As far as possible tension members should be so arranged that they are not subjected to bending from eccentricity of connections. If this condition is satisfied, the stress distribution across the net section will be uniform. Where a joint is made the maximum proportion of the member surface should be attached to be gusset plate or the splice plate.

A lot of choice is available about a variety of sections suitable for use as tension members. We must plan the design to take full advantage of the selected section. For instance, welded plates are economical when members are box shaped or tubular.

For welded trusses of moderate spans structural tubing may work out to be economical Box shaped members can be fabricated in the workshop and can be used for long pans. In bolted trusses, tension members need additional considerations. In the case of the angle or tee about fifty per cent of the unconnected leg only is found to be effective, due to the eccentric connection to the gusset plate.

To reduce the loss of sectional area due to bolt holes, it is desirable to provide the bolts in a staggered manner.

Many practical and site conditions influence the choice of suitable sections for a steel structure. The choice to a great extent depends on the type of loading and the type of connections desirable. When ends of members are meant to be connected by bolts, the best choice would be angles and channels. These sections are also convenient when built-up sections are to be made.

When welded connections are preferred plates and angles are most suitable. Single angles are commonly used for making light trusses. They are also used as bracings. Steel rods can be used as suspenders for suspension bridges. They can also be used to make small span trusses. Built-up sections are used in making large span and heavily loaded bridge trusses. Tubular sections are used to make long span light structures.

There is no doubt that it is desirable to ensure that the load should be transmitted to a tension member so as to act along the longitudinal centroidal axis of the member. But this may not be possible always. A common example is the case of a truss members at a joint. It is not practically possible to arrange the members at a joint so that the longitudinal centroidal axes of all the members converge exactly at the joint.

The members are therefore subjected to small moments due to eccentric transmission of forces to the members. Such moments are of small magnitude and are not considered in the designs. Another instance is that of a single angle connected to the gusset plate at a joint.

In this case the longitudinal axis of the member lies outside the cross-section resulting in eccentric load transmission and a consequent moment. This moment however is not too small to be ignored and is considered by making suitable provision in determining the design tensile strength by the I.S. code.

#### Slenderness Ratio for Tension Members:

Though not from the point of view of strength the slenderness ratio of a tension member has to be within certain limits to avoid-

(i) Excessive sag due to self-weight of the member

(ii) Flutter due to wind

(iii) Vibrations caused by moving loads.

Sometimes a tension member may be subjected to a comprehensive force in a possible load reversal situation. Slenderness ratio limitation becomes relevant in a such a condition also. Limits for slenderness ratios for tension members are given in below table.

#### Block Shear Failure and Shear Drag of Tension Member:

Tests have shown that connections of angles, plates and coped beams are liable to fail as a consequence of block shear. This is type of failure where the member develops a shear failure along a row of bolt holes parallel to the direction of the load along with a tension failure on a perpendicular face.

Block failure of a plate connected to a gusset plate with two rows of bolts.

Fig. 6.16 shows a plate in tension connected to a gusset plate. When a block shear failure of the plate occurs, the plate develops a shear along the bolt holes 1 – 2 and 4 – 3 and a tension failure along 2 – 3.

Block shear failure of an angle connected to a gusset plate with one row of bolts-

Fig. 6.17 shows an angle in tension connected to a gusset plate with one row of bolts. In this case the angle develops a shear failure along the bolt line 1 – 2 and a tension failure along 2-2.

The IS code (IS 800) has given the following formula tor the block shear strength Tdb of the connection.

where,

Avg, Avn = Minimum gross and net area in shear along bolt line parallel to external force respectively.

Atg, Atn = Minimum gross and net area in tension from the bolt hole to the toe of the angle end bolt line perpendicular to the line of force respectively.

ƒu, ƒy = Ultimate and yield stress of the material respectively.

Note:

Block shear failure can be prevented by increasing the spacing between bolts.

Tensile force gets transmitted 10 members like angles, channels and in some cases I-sections from gusset plates or other connecting elements. In a single angle member the tensile force is transmitted to the connected leg. In the regions close to the joint stresses in the connected leg are higher than in the outstanding leg. At sections farther away the stress distribution becomes uniform. This gradual transfer of stress to the outstanding leg is by shear action. There are chances of the member to fail due to excessive stresses in the connected leg.

Similarly for an I-section tension member to which a tensile force is transmitted from the connecting plates connected to the flanges, the stresses in the flanges will be higher than in the web. At sections far from the connected region the stress distribution becomes even. This phenomenon where in a certain distance from the first bolt the stress distribution becomes uniform is called shear drag.

#### Failure Modes for Tension Members:

A tension member is liable to fail in various modes and the section of the member should be designed to prevent failure by any of these modes.

The I.S. 800 code has suggested to consider the following modes of failure:

(i) Failure by yielding of the gross-section.

(ii) Failure of the net section by rupture.

(iii) Block shear failure in which a certain part of the member at the connected end is sheared out from the rest of the member.

For a safe design, the factored tension should be less than the design strength in tension which is the least of, the design strength in yielding design strength in rupture and the design strength in block shear.

Strength Affected by Bolt Holes:

Tension members are often connected to gusset plates or other members by bolted connections. Due to the bolt holes the resisting sectional area of the member is decreased resulting in decrease in strength of the members. Then strength of the member is also affected due to the method adopted in making bolt holes. Bolt holes can be made by punching or drilling.

When holes are made by punching the material close to the hole gets weekend, and loses ductility. Besides these there will be stress concentrations in the material close to the punched holes. Members punched for bolt holes lose their strength under the action of pulsating loads.

These defects will be absent when holes are made by drilling. Hence for all structural connections bolt holes should preferably be done by drilling.

#### Design Strength of a Tension Member:

Design Strength Due to Yielding of Cross-Section:

A tension member has to be designed so that its cross-sectional area is sufficient to resist the tensile load on the member. We generally make reference to gross and net section of the member. The gross- section means the original cross-section of the member.

The net section means the reduced section at a line of bolts and is equal to the gross-sectional area minus the allowance for bolt holes. Bolts are generally provided in clearance holes of diameter usually 2 mm more than the diameter of bolts (for bolt diameters up to 24 mm).

It may first appear that since some material is absent at the net section a failure is most likely at the net section only. But the important aspect in the design is, that it is desirable that the gross-section yields before ultimate stress is reached at the net section.

As per IS code (IS 800) the design strength in axial tension governed by yielding of the gross-section is given by-

Tdg = (Agƒy)/γmo

where,

ƒy = Yield stress of the material

Ag = Gross area of cross-section

γmo = Partial safety factor for failure by yielding = 1.10

(i) Plates:

The design strength in tension of a plate Tdn as governed by rupture of net cross-sectional area An at the holes is given by-

where,

ƒu = Ultimate stress of the material

An = Net effective area of the plate

γml = Partial safety factor for failure at ultimate stress = 1.25

The net effective area of the plate is given by-

where,

b, t = Width and thickness of the plate respectively.

do = Diameter of the bolt hole (2 mm in addition to the diameter of the bolt in case of directly punched holes)

g = Gauge length between the bolt holes, as shown in Fig. 6.14.

ps = Staggered pitch length between line of bolt holes as shown in Fig. 6.14.

n = Number of bolt holes in the critical section, and

i = Subscript for summation of all the inclined legs.

The design strength of threaded reds in tension Tdn as governed by rupture is given by-

where, An = Net root area at the threaded section.

(iii) Single Angles:

The rupture strength of an angle connected through one leg is affected by shear lag. The design strength, Tdn as governed by rupture at net section is given by-

where,

w = Outstand leg width

bs = Shear leg width as shown in Fig. 6.15

Lc = Length of the end connection, that is the distance between the outer most bolts in the end joint measured along the load direction or the length of weld along the load direction.

For preliminary sizing, the rupture strength of net section may be approximately taken as-

where,

α = 0.6 for one or two bolts, 0.7 for three bolts and 0.8 for four or more bolts along the length in the end connection or equivalent weld length,

An = Net area of the total cross-section,

Anc = Net area of the connected leg

Ag0 = Gross area of the outstanding leg, and

t = Thickness of the leg.

The rupture strength Tdn of double angles, channels, I-sections and other rolled steel sections connected by one or more elements to an end gusset is also governed by shear lag effects. The design tensile strength of such sections as governed by tearing of net section may also be calculated using the equation given above. In this case β is calculated based on the shear lag distance bs taken from the farthest edge of the outstanding leg to the nearest bolt/weld line in the connected leg of the cross-section.

When such a member is subjected to tension, the web is found to be partially ineffective. Accordingly, the net effective area is taken as,

An = Gross area – area of bolt holes – half area of the web.

#### Factors Affecting the Design of a Tension Member:

A tension member is theoretically the most efficient structural element but the efficiency of the member is liable to be affected by the following factors:

(i) End Connections:

If the member is connected to a gusset plate by bolts then the bolt holes reduce the section of the member.

If the member is subjected to reversal of load the member may buckle since the tension member is a slender member.

(iii) Some tension members have to resist bending moment also in addition to the main axial tensile force. Such moments may be due to eccentricity of end connection or due to lateral load on the member.

When bolts or threaded bars are provided the strength of the member must be determined by the area corresponding to the root of the threads.

When a single angle is connected through one leg the outstanding leg will not be fully effective. Bolts provided in the connected legs reduce the section of the member.

Loss of section due to bolt holes can be avoided by providing full strength joints by welding. However during erection joints at site are made by bolting. Welding is mostly confined to shop joints.

Splices become necessary at sites to connect together large trusses fabricated in sections in the shop, for convenience in transport. Splices also become necessary in long members and also where the member section changes.

#### Positioning of Bolts in Angle Members:

As recommended by Bureau of Indian Standards SP: 6(1) the positioning of bolts in angle members shall be such as to provide the gauge distances given in the table below.