Unit – 3
Tension members
Introduction
When an anxiety member is subjected to axial tensile pressure, then the distribution of strain over the pass-segment is uniform. The complete internet place of a member is efficaciously used on the most permissible uniform strain. Therefore, a tensile member subjected to axial tensile pressure is used to be green and not pricey member. The method of the layout of an anxiety member is defined under with assist of instance problems.
Tension members are structural elements which are subjected to axial tensile forces. Examples of anxiety members are bracing for homes and bridges, truss members, and cables in suspended roof systems.
In an axially loaded anxiety member, the strain is given by:
F = P/A
wherein P is the importance of the burden and A is the pass-sectional place.
The strain given by this equation is exact, understanding that the pass segment isn't adjoining to the factor of utility of the burden nor having holes for bolts or other discontinuities. For instance, given an eight x 11. five plate this is used as an anxiety member (segment a-a) and is hooked up to a gusset plate with 7/eight-inch-diameter bolts (segment b-b):
Design
To layout anxiety members, it is crucial to examine how the member might fail beneath Neath each yielding (excessive deformation) and fracture, which can be taken into consideration the restriction states. The restriction nation that produces the smallest layout energy is taken into consideration the controlling restriction nation. It additionally prevents the shape from failure.
Using American Institute of Steel Construction standards, the last load on a shape may be calculated from one of the following combinations:
1.4 D
1.2 D + 1.6 L + 0.5 (Lr or S)
1.2 D + 1.6 (Lr or S) + (0.5 L or 0.8 W)
1.2 D + 1.6 W + 0.5 L + 0.5 (Lr or S)
0.9 D + 1.6 W
L= 14
the central problem of designing a member is to find a cross section for which the required strength doesn't exceed the available strength:
Pu < ¢ Pn where Pu is the sum of the factored loads.
to prevent yielding
0.90 Fy Ag > Pu
to avoid fracture,
0.75 Fu Ae > Pu
therefore, the design must consider the loads applied to this member, the design forces acting on this member (Mu, Pu, and Vu) and the point where this member would fail.
Types of anxiety participants
1. Wires and cables:
Wires ropes are completely used for hoisting functions and as guy wires in metal stacks and towers. Strands and ropes are shaped via way of means of helical winding of wires. A strand includes person wires wound helically around the important core. These aren't endorsed in bracing gadget as they cannot withstand compression. The benefits of twine and cable are flexibility and power.
2. Bars and rods:
These are most effective varieties of anxiety participants. Bars and rods are regularly used as anxiety participants in bracing gadget, as sag rods to aid purlins among trusses. Presently those aren't preferred of with the designers due to the fact massive drift they purpose in the course of sturdy winds and annoying noise induces via way of means of the vibrations. 3.Plates and flat bars: These are used regularly as anxiety participants in transmission towers, foot bridges, etc. These also are utilized in columns to hold the component participants of their accurate position. E.g.- lacing flats, batten plates, give up tie plates etc. Single and built-up structural shapes: 1. Open sections inclusive of angles, channels and I section. •Compound and built-up sections inclusive of double angles and double channels with are without extra plates and jointed with a few connections’ gadget. • Closed sections inclusive of circular, square, rectangular or whole sections.
3. Behavior of Tension Members The load-deformation conduct of participants subjected to uniform tensile pressure is just like the load-deflection conduct of the corresponding simple cloth. The common pressure-stress conduct of slight metal below axial tensile load is proven in Fig. 1. The higher yield factor is merged with the decrease yield factor for convenience. The cloth indicates a linear elastic conduct withinside the preliminary Behavior region (O to A). The cloth Behavior undergoes Behavior enough Behavior yielding Behavior in component A to B. Further deformation ends in a boom in resistance, in which the cloth stress hardens (from B to C). The cloth reaches its last pressure at factor C. The pressure decreases with boom in in addition deformation and breaks at D. The excessive power metal participants do now no longer showcase the properly described yield factor and the yield region (Fig. 1). For such materials, the 0.2 percentage evidence pressure is normally taken as the yield pressure (E).
STEPS TO BE FOLLOWED IN THE DESIGN OF A TENSION MEMBER
The following steps can be accompanied withinside the layout of axially loaded anxiety participants.
1. Corresponding to the loading on the shape of which the anxiety member is a part, the tensile pressure withinside the member is first computed.
2. The internet vicinity required for the member is decided via way of means of dividing the tensile pressure withinside the member via way of means of the permissible tensile pressure.
3. Now, an appropriate phase having gross vicinity approximately 20 in step with cent to twenty-five in step with cent extra than the predicted vicinity is decided on. For the member decided on deductions are made for the vicinity of rivet holes and the internet powerful vicinity of the phase is decided. If the internet vicinity of the phase of the member so decided is extra than the internet vicinity requirement predicted in step i, the layout is taken into consideration safe.
4. The slenderness ratio of an anxiety member shall now no longer exceed 400. In the case of an anxiety member vulnerable to reversal of pressure because of the motion of wind or earthquake, slenderness ratio shall now no longer exceed 350. If the reversal of pressure is because of masses others than wind or earthquake, the slenderness ratio shall now no longer exceed 180.
Example 1: Determine the tensile strength of the 12 mm thick plate shown in Fig 9.1. Rivets used for the connection are 20 mm diameter. Allowable tensile stress is 150 N/mm2.
Solution
Diameter of the rivet hole = 20 + 1.5 = 21.5 mm
The critical section to be considered is a section like ABCDE.
Effective width at critical section = b – nd = 180 – (3 x 21.5) = 115.5 mm
Effective net area = 115.5 x 12 mm2 = 1386 mm2
Strength of plate = 1386 x 150 = 207900 N = 207.9 kN.
Example 2: Find the strength of the 12 mm thick plate shown in Fig. 9.2. All the holes are 21.5 mm as gross diameter. Take ft=150 N/mm2.
Solution
Gross diameter of rivet hole = 21.5 mm
The effective net width will be computed along the various chain lines
Staggered pitch p = 40 mm
Gauge distance g = 50 mm
Net width corresponding to the chain ABCD = 210 – (2 x 21.5) = 167 mm
Net width corresponding to the chain ABECFG
Net width corresponding to the chain ABEFG
Net width corresponding to the chain ABECD
Therefore minimum net width = 148mm
Safe load = Safe stress × Area of minimum net effective section
Example 3: The tension member of a roof truss consists of two unequal angles 70 x 45 x 8 with the longer legs connected by 16 mm diameter rivets. Find the safe tension for the member, the angles being one on either side of the gusset plate.
Solution
Gross area of 2 angles, 70 x 45 x 8= 1,712 mm2
Area of 2 rivet holes, 2 x (16 + 1.5) x 8 = 280 mm2
Net area of the member, 1712 – 280 = 1,432 mm2
Therefore, safe tension for the member = 150 x 1432 = 2,14,800 N = 214.8 kN.
Shear Lag
The tensile pressure to an anxiety member is transferred via way of means of a gusset plate or via way of means of the adjoining member linked to one of the legs both via way of means of bolting or welding. This pressure that's transferred to at least one leg via way of means of the cease connection regionally gets transferred as tensile pressure over the whole move segment via way of means of shear. Hence, the distribution of tensile pressure at the segment from the primary bolt hollow to the ultimate bolt hollow will now no longer be uniform. Hence, the linked leg will have better stresses at failure even as the stresses withinside the superb leg might be noticeably lower. However, at sections some distance far from the cease connection, the pressure distribution turns into extra uniform. Here the pressure switch mechanism, i.e., the inner switch of forces from one leg to the other (or flange to web, or from one component to the other), other), might be via way of means of shear and due to the fact due to the fact one component ‘lags’ at the back of the other, the phenomenon is cited as ‘shear lag’. The shear lag reduces the effectiveness of the issue plates of an anxiety member that aren't linked without delay to a gusset plate. The performance of an anxiety member may be multiplied via way of means of lowering the location of such additives which aren't without delay linked on the ends. The shear lag effect reduces with boom withinside the connection length.
1. Modes of Failure The extraordinary modes of failure in anxiety contributors are
1. Gross segment yielding
2. Net segment rupture
3. Block shear failure
In IS-800:2007, we do follow the following steps to determine the tension capacity of the section.
6.33 Single Angles
The rupture Strength of an angle connected through one leg is affected by shear lag. The design strength, 
, as governed by rupture at net section is given by:
Where
What is happening in the above formula, the capacity of the connected leg and outstanding leg are separately calculated. The assumption here is that the outstanding leg will reach yielding stress when the connected leg probably would have attained the ultimate stress.
The net area is calculated for the connected leg to determine its capacity. The area of the outstanding leg is reduced with the reduction factor "β", which is our shear lag factor. It depends on the factors like the length (L) of the connection and shear lag width (bs).
Alternatively, a simpler approach is also provided in IS-800:2007 as shown in the snap below.
For preliminary sizing, the rupture strength of net section may be approximately taken as:
Where
= 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;
net area of the total cross-section;
net area of the connected leg;
=gross area of the outstanding leg; and
thickness of the leg.
Here, the net sectional area is multiplied with the reduction factor "α" to account for the shear lag based on the number of bolts used in the connection (Length of the connection).
As we have seen the concept of shear lag and the factors affecting it, the following are my inference
Lug Angles
Lug angles are sometimes used to reduce the length of connections. Figure below shows the lug angle connection with single or a channel type of tension member.
Due to the possible deformation of the outstanding leg of the lug angle, the rivets connecting the gusset plate with the lug angle will share less load than the rivets connecting the main member with the gusset plate.
The India Standard IS 800 specifies the subsequent for the layout of lug angles:
A(net) = Gross place – deduction for holes
Compression contributors are structural factors which can be driven collectively or bring a load, extra technically they're subjected best to axial compressive forces. That is, the masses are implemented at the longitudinal axis via the centroid of the member pass segment, and the load over the pass sectional place offers the pressure at the compressed member. In homes, posts and columns are nearly continually compression contributors as are the top chord of trusses.
A structural member loaded axially in compression is normally referred to as a compression member. Vertical compression contributors in homes are referred to as columns, posts or stanchions. A compression member in roof trusses is referred to as struts and in a crane is referred to as a boom. Columns which
are short are subjected to crushing and behave like members under pure compression. Columns which are long tend to buckle out of the plane of the load axis.
The most important styles of column bases are the following:
(i) Slab base
(ii) Gusseted base
(i) Slab Base:
In this association the column stands at once over a metal base plate which rests over a concrete basis. The base plate is attached to the column flanges with connecting angles with the aid of using welding or bolting. The column-base plate unit is geared up withinside the concrete basis with basis bolts.
(ii) Gusseted Base:
Gusseted base plates are used for columns sporting heavy loads. In this example fastenings are used to connect the bottom plate and the column withinside the shape of gusset plates, angles etc.
Compression contributors of roof trusses are composed of unmarried angles or double angles. These contributors can be non-stop contributors (just like the fundamental rafter of the roof truss) or discontinuous contributors (just like the vertical and diagonal contributors of the truss).
The powerful duration KL of the compression contributors can be taken as zero.7 to 1. zero instances the space among centers of connections relying at the diploma of cease restraint provided. In the case of contributors of trusses for buckling withinside the aircraft perpendicular to the aircraft of the truss, the powerful duration, KL will be taken as the space among the centers of intersection.
Angle Struts of Compression Members:
Single Angle Struts:
The compressive pressure in unmarried perspective can be transferred both concentrically to its centroid via cease gusset or eccentrically with the aid of using connecting one in all its legs to a gusset or adjacent member.
Concentric Loading:
When an unmarried perspective is concentrically loaded in compression, the layout power can be decided as withinside the case of axially loaded columns.
COMMON SECTIONS OF COMPRESSION MEMBERS
The not unusual place sections used for compression contributors are proven in Fig. with their approximate radii of gyration. A column or a compression member can be made of many different sections to guide a given load. Few sections fulfill realistic requirement in a given case. A tubular phase is maximum green and comparatively cheap for the column unfastened to buckle in any route. The radius of gyration r for the tubular phase in all of the instructions stays identical. The tubular phase has excessive local buckling power. The tubular sections are appropriate for medium loads. However, it's miles hard to have their cease connections. A stable spherical bar having a cross-sectional place identical to that of a tubular phase has radius of gyration, r a great deal smaller than that of tube. The stable spherical bar is much less comparatively cheap than the tubular phase. The stable spherical bar is higher than the skinny rectangular phase or a flat strip. The radius of gyration of flat strip approximately its narrow route could be very small. Theoretically, the rods and bars do face up to some compression. When the duration of structural member is set three m, then the compressive strengths of the rods and bars are very small.
Single perspective sections are not often used besides in mild roof trusses, due to eccentricity on the cease connections. Tee-sections are frequently utilized in roof trusses. The unmarried rolled metal I-phase and unmarried rolled metal channel phase are seldom used as column. The fee of radius of gyration r, approximately the axis parallel to the web is small. The intermediate extra helps withinside the susceptible route make the use of those sections comparatively cheap. Sometimes the usage of I-sections and channel sections are favored due to the technique of rolling on the mills, since, the out-to-out dimensions stay identical for a given depth. This failure is not there with different rolled metal sections. The charges of unmarried rolled metal sections according to unit weight are much less than the ones of constructed-up sections. Therefore, the unmarried rolled metal sections are favored as long as their use is feasible.
STRENGTH OF COMPRESSION MEMBERS
The power of a compression member is described as its secure load sporting potential. The power of a centrally loaded immediately metal column relies upon at the powerful cross-sectional place, radius of gyration (viz., form of the cross-phase), the powerful duration, the importance and distribution of residual stresses, annealing, out of straightness and bloodless straightening. The powerful cross-sectional place and the slenderness ratio of the compression contributors are the primary features, which have an effect on its power. In case, the allowable stress is thought to differ parabolically with the slenderness ratio, it could be proved that the performance of a form of a compression member is associated with A/r2. The performance of a form is described because the ratio of the allowable load for a given slenderness ratio to that for slenderness ratio identical to zero. The secure load sporting potential of compression member of recognised sectional place can be decided as follows:
Step 1. From the actual duration of the compression member and the guide situations of the member, that are recognised, the powerful duration of the member is computed.
Step 2. From the radius of gyration approximately diverse axes of the phase given in phase tables, the minimum radius of gyration (rmin) is taken. rmin for a constructed-up phase is calculated.
Step three. The most slenderness ratio (l/ rmin) is decided for the compression member.
Step 4. The allowable running stress (σac) withinside the route of compression is found similar to the most slenderness ratio of the column from IS:800-1984.
Step 5. The powerful sectional place (A) of the member is stated from structural metal phase tables. For the constructed-up contributors it could be calculated.
Step 6. The secure load sporting potential of the member is decided as P= (σac. A), where P=secure load
Example 1 A single angle discontinuous strut ISA 150 mm x 150 mm x 12 mm (ISA 150 150, @0.272 kN/m) with single riveted connection is 3.5 m long. Calculate safe load carrying capacity of the section.
Solution:
Step 1: Properties of angle section
ISA 150 mm x 150 mm x 12 mm (ISA 150 150, @0.272 kN/m) is used as discontinuous strut. From the steel tables, the geometrical properties of the section are as follows:
Sectional area A = 3459 mm2
Radius of gyration rxx= ryy=149.3 mm
Radius of gyration ruu= 58.3 mm, rvv=29.3 mm
Step 2: Slenderness ratio,
Minimum radius of gyration rmin= 29.3 mm
Effective length of strut l= 3.5 m
Slenderness ratio of the strut
Step 3: Safe load
From IS:800-1984 for l/r=119.5 and the steel having yield stress, fy=260 N/mm2, allowable working stress in compression σac =64.45 N/mm2 (MPa)
For single angle discontinuous strut with single riveted connection, allowable working stress
0.80 σac = (0.80 x 64.45) = 51.56 N/mm2.
The safe load carrying capacity
Example 2 In case in Example 1, a discontinuous strut 150 x 150 x 15 angle section is used, calculate the safe load carrying capacity of the section.
Solution:
Step 1: Properties of angle section
Angle section 150 mm x 150 mm x 15 mm is used as discontinuous strut. From the steel tables, the geometrical properties of the section are as follows:
Sectional area A = 4300 mm2
Radius of gyration rxx= ryy=45.7 mm
Radius of gyration ruu= 57.6 mm, rvv=29.3 mm
Step 2: Slenderness ratio,
Minimum radius of gyration rmin= 29.3 mm
Effective length of strut l= 3.5 m
Slenderness ratio of the strut
Step 3: Safe load
From IS:800-1984 for l/r=119.5 and the steel having yield stress, fy=260 N/mm2, allowable working stress in compression σac =64.45 N/mm2 (MPa)
For single angle discontinuous strut with single riveted connection, allowable working stress
0.80 σac = (0.80 x 64.45) = 51.56 N/mm2.
The safe load carrying capacity
Example 3 In Example 1, if single angle discontinuous strut is connected with more than two rivets in line along the angle at each end, calculate the safe load carrying capacity of the section.
Solution:
Step 1: Properties of angle section
Discontinuous strut ISA 150 mm x 150 mm x 12 mm (ISA 150 150, @0.272 kN/m) is used with double riveted connections. From the steel tables, the geometrical properties of the section are as follows:
Sectional area A = 3459 mm2
Radius of gyration rxx= ryy=149.3 mm
Radius of gyration ruu= 58.3 mm, rvv=29.3 mm
Length of strut between center to center of intersection L=3.50 m
Step 2: Slenderness ratio,
Minimum radius of gyration rmin= 29.3 mm
Effective length of discontinuous strut double riveted 0.85 x L= 0.85 x 3.5 = 2.975 m
Slenderness ratio of the strut
Step 3: Safe load
From IS:800-1984 for l/r=101.5 and the steel having yield stress, fy=260 N/mm2, allowable working stress in compression σac =71.65 N/mm2 (MPa)
Allowable working stress for discontinuous strut double riveted is not reduced.
The safe load carrying capacity 
Example 4 A double angle discontinuous strut ISA 125 mm x 95 mm x 10 mm (ISA 125 95, @0.165 kN/m) long legs back-to-back is connected to both the sides of a gusset plate 10 mm thick with 2 rivets. The length of strut between center to center of intersections is 4 m. Determine the safe load carrying capacity of the section.
Solution:
Step 1: Properties of angle section
The double angle discontinuous strut 2 ISA 125 mm x 95 mm x 10 mm (ISA 125 95, @0.165 kN/m) is shown in Fig. 11.4. Assume the tacking rivets are used along the length. From the steel tables, the geometrical properties of (two angle back-to-back) the sections are as follows:
Sectional area A = 4204 mm2
Radius of gyration rxx= 39.4 mm
Angles are 10 mm apart
Radius of gyration ryy= 40.1 mm
Length of strut between center to center of intersection L=4 m
Step 2: Slenderness ratio,
Minimum radius of gyration rmin= 39.4 mm
Effective length of discontinuous strut 0.85 x L= 0.85 x 4.0 = 3.40 m
Slenderness ratio of the strut
Step 3: Safe load
From IS:800-1984 for l/r=86.3 and the steel having yield stress, fy=260 N/mm2, allowable working stress in compression σac =95.96 N/mm2 (MPa)
The safe load carrying capacity
ANGLE STRUTS
The compression members consisting of single sections are of two types:
Continuous members
The compression members (consisting of single or double angles) which are continuous over a number of joints are known as continuous members. The top chord members of truss girders and principal rafters of roof trusses is continuous members. The effective length of such compression members is adopted between 0.7 and 1.0 times the distance between the centers of intersections, depending upon degree of restraint provided. When the members of trusses buckle in the plane perpendicular to the plane of the truss, the effective length shall be taken as 1.0 times the distance between the points of restraint. The working stresses for such compression members is adopted from IS:800-1984 corresponding to the slenderness ratio of the member and yield stress for steel.
Discontinuous members
The compression members which are not continuous over a number of joints, i.e., which extend between two adjacent joints only are known as discontinuous members. The discontinuous members may consist of single angle strut or double angle strut. When an angle strut is connected to a gusset plate or to any structural member by one leg, the load transmitted through the strut, is eccentric on the section of the strut. As a result of this, bending stress is developed along with direct stress. While designing or determining strength of an angle strut, the bending stress developed because of eccentricity of loading is accounted for as follows:
i. Single angle strut
ii. Double angle strut
If the struts carry in addition to axial loads, loads which cause transverse bending, the combined bending and axial stress shall be checked as described for the columns subjected to eccentric loading. The tacking rivets should be provided at appropriate pitch.
The tacking rivets are also termed as stitching rivets. In case of compression members, when the maximum distance between centers of two adjacent rivets exceeds 12 t to 200 mm whichever is less, then tacking rivets are used. The tacking rivets are not subjected to calculated stress. The tacking rivets are provided throughout the length of a compression member composed of two components back-to-back. The two components of a member act together as one piece by providing tacking rivets at a pitch in line not exceeding 600 mm and such that minimum slenderness ratio of each member between the connections is not greater than 40 or 0.6 times the maximum slenderness ratio of the strut as a whole, whichever is less.
In case where plates are used, the tacking rivets are provided at a pitch in line not exceeding 32 times the thickness of outside plate or 300 mm whichever is less. Where the plates are exposed to weather the pitch in line shall not exceed 16 times the thickness of the outside plate or 200 mm whichever is less. In both cases, the lines of rivets shall not be apart at a distance greater than these pitches.
The single angle sections are used for the compression members for small trusses and bracing. The equal angle sections are more desirable usually. The unequal angle sections are also used. The minimum radius of gyration about one of the principal axis is adopted for calculating the slenderness ratios. The minimum radius of gyration of the single angle section is much less than the other sections of same cross-sectional area. Therefore, the single angle sections are not suitable for the compression member of long lengths. The single angle sections are commonly used in the single plane trusses (i.e., the trusses having gusset plates in one plane). The angle sections simplify the end connections.
The tee-sections are suitable for the compression members for small trusses. The tee-sections are more suitable for welding.
Key Takeaways:
A(net) = Gross place – deduction for holes
3. These are most effective varieties of anxiety participants. Bars and rods are regularly used as anxiety participants in bracing gadget, as sag rods to aid purlins among trusses.
References:
1. McCormac, J.C., Nelson, J.K. Jr., Structural Steel Design. 3rd edition. Prentice Hall, N.J., 2003.
2. Galambos, T.V., Lin, F.J., Johnston, B.G., Basic Steel Design with LRFD, Prentice Hall, 1996
3. Segui, W. T., LRFD Steel Design, 2nd Ed., PWS Publishing, Boston.
4. Salmon, C.G. and Johnson, J.E., Steel Structures: Design and Behavior, 3rd Edition, Harper & Row, Publishers, New York, 1990.
5. Related Codes of Practice of BIS
6. NBC, National Building Code, BIS (2017).
7. ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-02, American Society of Civil Engineers, Virginia, 2002.
8. Subramanian, N. (2010). Steel Structures: Design and Practice, Oxford University Press.
9. Duggal, S.K. (2014). Limit State Design of Steel Structures, McGraw Hill.
