STRUCTURAL MEMBER DESIGN BASED ON IS: 800 (LIMIT STATE METHOD)

Dr. T. K. Bandyopadhyay **1.0 INTRODUCTIONBeams and columns form the two main components which constitute a structure, and serves the basic purpose of supporting and transmitting the entire loading both vertical and horizontal for which the overall structure is intended, to the ground or earth through the adequately designed foundation system.

In a steel structure, there are other equally important structural components, which govern the satisfactory performance of the entire structure like the bracing systems, both vertical column bracings and also the horizontal floor bracings and most of all the connections between structural components. Beams are generally subjected only to flexure about the horizontal axis whereas columns are subjected to axial load along with bending moment about the major axis. The minor axis moment in columns are generally nil or very nominal since in a standard structural system, the columns are so oriented that the frames along the major axis of the columns are moment resistant frames, and column bracings are provided in the frames along the other perpendicular direction.

This paper is devoted entirely to the procedures involved in designing various structural components like “Tension Members”, “Compression Members” and “Beams subjected to flexure”. Typical problems have been solved using “Allowable Stress Design” method as per the existing IS: 800 – 1984 as well as the “Limit State Method” as have been introduced in the draft IS: 800 (LSM version).

The Limit state Method (LSM) of design adopted herein is under approval of the Bureau of Indian Standards.

2.0 LOADS AND LOAD COMBINATIONS

To design a structure, it is analyzed first for its intended structural configuration and assumed sectional properties against various loads individually and in combination with each other in a way by which the structure may be subjected any time or at all time during the life of the structure for which it is to be built.

The various primary loads and other secondary effects required to be considered for Indian conditions while computing the maximum stresses in a structure or structural components are mainly as follows:a) Dead Loads as per IS: 875 – 1987 (Part – 1).b) Imposed or Live Loads as per IS: 875 – 1987 (Part – 2).c) Wind Loads as per IS: 875 – 1987 (Part – 3).d) Seismic or Earthquake loads as per IS: 1893 – 2002.e) Erection loads.------------------------------------------------------------------------------------------------------------** Dr. T. K. Bandyopadhyay, Jt. Director General;

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Institute for Steel Development and Growth, 52/1A Ballygunge Circular Rd, Kolkata - 700 019Secondary effects due to contraction or expansion resulting from temperature changes, shrinkage, creep in compression members, differential settlements of the structure as a whole and its components.

As a general approach, a structure is analyzed for all the probable primary load cases and their combinations as mentioned above. Only for special structures or under stringent conditions, the secondary effects are considered in the overall analysis and in the design of connections of the structural components.

The Load combinations which are applicable for a standard structure as per Indian codes are as given below:

a) Dead Load (DL)b) Dead Load (DL) + Live Load (LL)c) Dead Load (DL) + Wind Load (WL) / Earthquake Load (EL)d) Dead Load (DL) + Live Load (LL) + Wind Load (WL) / Earthquake Load (EL)

While designing a structure using the popular “Allowable stress Design method”, the above load combinations are considered with an individual load factor of unity. As per existing IS: 800 -1984, the permissible stress limit as calculated is allowed to be increased by 33% in case of load combinations, which considers wind or seismic load.

In the proposed Limit State Method of design also the above load combinations are considered, but with variable load factors called the “Partial Safety Factor for Loads as described in Table – 1 below. This variable load factors basically ensures a rational approach to account for the variable nature of the loadings and thus enable to use steel efficiently and economically in different structural systems.

Similarly, to determine the strength of the member to be designed against the factored load as described above, a reduction factor for strength called “Partial Safety Factor for Material” is taken into consideration, which accounts for uncertainty in material strength and quality as well as manufacturing tolerances. Various material safety factors as have been adopted in IS: 800 (LSM) to cater to the Indian conditions are as given in Table – 2.

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Table – 1: Partial Safety Factors for Loads f for Limit States

Combination

Limit State of Strength Limit State of Serviceability

DL

LLWL /EL

AL DL

LLWL / ELMain

Accompanying(CL, SL**,

etc.)Main

Accompanying(CL, SL**,

etc.)DL+LL+CL 1.5 1.5 1.05 - - 1.0 1.0 1.0 -DL+LL+CL +WL/EL

1.21.2

1.21.2

1.050.55

0.61.2

- 1.0 0.8 0.8 0.8

DL+WL/EL1.50.9*

- - 1.5 - 1.0 - - 1.0

DL + Erection Load

1.20.9*

1.2 - - - - - - -

DL + LL + Accident Load

1.0 0.35 0.35 - 1.0 - - - -

* This value is to be considered when stability against overturning or stress reversal is critical** SL is Snow Loads

Table – 2 Partial Safety Factor for Materials, m

Sl. No.

Definition Partial Safety Factor

1 Resistance, governed by yielding mo 1.102 Resistance of member to buckling mo 1.103 Resistance, governed by ultimate stress m1 1.25

4 Resistance of connection m1Shop

FabricationField

fabrication(i) Bolts – Friction Type, mf 1.25 1.25(ii) Bolts – Bearing Type, mb 1.25 1.25(iii) Rivets 1.25 1.25(iv) Welds 1.25 1.50

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3.0 DESIGN PROCEDURES

The detail procedures for designing various structural members e.g. tension members, compression members, and members subjected to flexure using the allowable stress design method as per IS: 800 – 1984 and also the Limit State Method of design as proposed in the draft IS: 800 (LSM version) have been discussed with the help of a few examples. These have been worked out to make the designer acquainted with the limit state method, as well as to get an idea about the level of economy and accuracy that may be attained in the Limit State Method of design. The examples have been included giving references to the clauses of both IS: 800 – 1984 and draft IS: 800 (LSM version) for WSM and LSM design respectively.

3.1 DESIGN OF TENSION MEMBER

3.1.1 Example – 1: Comparison of strength of a standard angle say ISA 50x50x6 for WSM and LSM subjected to load combination of dead load and live load.

Gross area of ISA 50x50x6, Ag = 5.68 cm2

(a) WSM (Welded) (Clause: 4.2.1 of Page –37 0f IS: 800 –1984)

An = A1+A2.k = (1+k) Ag/2 = 1.75 x 5.68/2 = 4.97 cm2 (A1=A2=Ag/2)

k = = 0.75, where A1, A2 are connected and out standing legs

Strength of section = 1500 x 4.97 / 1000 = 7.466 T

(b) WSM (Connected with 5 nos. 12 mm bolts)

A1 = 5.68/2 - 1.35 x 0.6 = 2.03 cm2; A2 = 5.68/2 =2.84 cm2

k =

Td = (2.03 + 0.682 x 2.84) 1500 = 5.95 T

(a1) LSM (connected with Weld) (Clause 6.1 of draft IS: 800 [LSM])(Permissible load is governed by smaller of strength obtained by (i) yielding of gross section, (ii) tearing at net section and (iii) block shear failure for bolted connection])

(i) Strength as governed by yielding of gross section (Clause 6.2) –

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Tdg = Ag.fy/γmo = 5.68x2500/1.10 =12.909 T

(γmo = safety factor for material against yield stress = 1.10)

(ii) Strength as governed by tearing at net section (Clause 6.3.3.)-The tearing strength of an angle connected through one leg is affected by shear lag. The design strength as governed by tearing at net section is given by

Tdn = 0.9Anc fu / m1+ Ago fy / mo.

(γmo = as discussed earlier)(γm1 = safety factor for material against ultimate stress = 1.25)

= 1.4 – 0.076 (w/t) (fy/fu) (bs/Lc ) = 1.4 – 0.076x (50/6) x (250/410) x (50/140) = 1.262L= length of 6mm weld = 140 mm, bs = w =50 mm]

Tdn =

Therefore, design strength is Tdn = 12.909 T

Comparison of LSM and WSM for Welded Connection:-

Now, comparing (a) with (a1). We find that for WSM, Td = 7.47T Equivalent load in LSM with load factors of 1.5 for DL & LL in DL+LL combination is Td = 7.47 x 1.5 = 11.205 T

Therefore, corresponding to WSM design, percentage strength attained in LSM is = 11.205/12.909 =0.868 or 86.8%

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bs = w

w

w1

w

bs = w + w1

(b1) LSM (Connected with 5 x 12 mm bolt)

(i) Strength as governed by yielding of gross section (Clause 6.2) –Tdg = Ag.fy/mo = 5.68x2500/1.10 =12.909 T

(ii) Strength as governed by tearing at net section (Clause 6.3.3) - Tdn = 0.9Anc fu / m1+ Ago fy / mo

= 1.4 – 0.076 (w/t) (fy/fu) (bs/Lc ) = 1.4 – 0.076x(50/6)x(250/410)x(72/120) = 1.168,L= length of connection = 30x4=120mm, bs = 50+28-6=72mm; w = 50mm]

Tdn =

(iii) Strength as governed by block shear failure (Clause 6.4) - (case – 1)

(case – 2

(Avg, Avn = minimum gross and net area in shear along the line of transmitted force, respectively Atg, Atn = minimum gross and net area in tension from the hole to the toe of the angle or next last row of bolt in plates, perpendicular to the line of force, [Length of connection = 25(edge distance)+30x4=145mm]Avg = 145x6 mm2: Avn = (145-4.5x13.5) x 6 mm2; Atg = 22x6 mm2; Atn = (22- 13.5/2) x 6 mm2)Therefore, design strength is Tdn = 11.615 T

Comparison of LSM and WSM for Bolted Connection:-

Now comparing (b) with (b1), we find that for WSM, Td = 5.95T

Equivalent load in LSM with load factors of 1.5 for DL & LL in DL+LL combination is Td = 5.95 x 1.5 = 8.925 T

Therefore, corresponding to WSM design, percentage strength attained in LSM is = 8.925/11.615 =0.768 or 76.8%

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Example – 2: Comparison of strength of a standard angle say ISA 90x90x8 for WSM and LSM subjected to load

combination of dead load, live load and wind load.

Gross area of ISA 90x90x8, Ag = 13.79 cm2

(a) WSM (Welded) (Clause: 4.2.1 of Page –37 of IS: 800 –1984)

An = A1+A2.k = (1+k) Ag /2 = 1.75 x 13.79/2 = 12.066 cm2 (A1=A2=Ag/2)

k = = 0.75

Strength of section = 1.33x1500 x 12.066 / 1000 = 24.072 T

(b) WSM (Connected with 6 nos. 16 mm bolts)

A1 = 13.79/2 -1.75 x 0.8 = 5.495 cm2 ; A2 = 13.79/2 =6.895 cm2

k =

Td = (5.495 + 0.705 x 6.895) 1500/1000 = 15.535T

(a1) LSM (connected with Weld) (Clause 6.1 of draft IS: 800) -

(i) Strength as governed by yielding of gross section (Clause 6.2)–Tdg = Ag.fy/mo = 13.79 x2500/1.10 = 31.34 T

(ii) Strength as governed by tearing at net section(Clause 6.3.3) -Tdn = 0.9Anc fu / m1+ Ago fy mo

Tdn =

= 1.4 – 0.076 (w/t) (fy/fu) (bs/Lc ) = 1.4 – 0.076x(90/8)x(250/410)x(90/200) = 1.165,L= length of 8 mm weld = 200mm, bs =90mm]

Therefore, design strength is Tdn = 31.34 T

Comparison of LSM and WSM for Welded Connection:-

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Now, comparing (a) with (a1). We find that for WSM, Td = 24.072 T Equivalent load in LSM with load factors of 1.2 for DL, LL and WL in DL+LL+WL combination is Td = 24.072 x 1.2 = 28.886 T

Therefore, corresponding to WSM design, percentage strength attained in LSM is = 28.886/31.34 =0.92 or 92%.

(b1) LSM (Connected with 6 x 16 mm bolt)

(i) Strength as governed by yielding of gross section Clause 6.2) –Tdg = Ag.fy/mo = 13.79 x2500/1.10 = 31.34 T

(ii) Strength as governed by tearing at net section (Clause 6.3.3) - Tdn = 0.9Anc fu / m1+ Ago fy /mo

Tdn =

= 1.4 – 0.076 (w/t) (fy/fu) (bs/Lc ) = 1.4 – 0.076 x(90/8)x(250/410)x(132/200) = 1.056,L= length of connection = 5 x 40 mm = 200 mm, bs=90+50 -8= 132mm; w = 90mm]

(iii) Strength as governed by block shear failure (Clause 6.4) - (Case – 1)

(Case – 2)

Therefore, design strength is Tdn = 24.83 T

Comparison of LSM and WSM for Welded Connection:-

Now comparing (b) with (b1), we find that for WSM, Td = 15.535 T

Equivalent load in LSM with load factors of 1.2 for DL, LL and WL in DL+LL+WL combination is Td = 15.535 x 1.2 = 18.642 T

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Therefore, corresponding to WSM design, percentage strength attained in LSM is = 18.64/24.83 =0.742 or 74.2%. Therefore, LSM is advantageous over WSM.

3.2 DESIGN OF COMPRESSION MEMBER

3.2.1 Example – 1: Design a member subjected to the following loads having a span of 5.0 meters.

DL = 45.0T, LL = 40T, WL = 30T

Load Combination (LSM) (As per table 5.1 of draft IS: 800)

(1) DL + LL = 1.5 x 45.0 + 1.5 x 40.0 = 127.50T

(2) DL + WL = 1.5 x 45.0 + 1.5 x 30.0 = 112.50T

(3) DL + LL + WL = 1.2 x 45.0 + 1.2 x 40.0 + 1.2 x 30.0 = 138.0T

The column at the bottom most level is considered for design The frame is a braced frame.

Length of the members, L = 5.0M

Let us consider ISMB 400 + 200 x 16 thk. PPF

(a) Design by WSM (Clause 5.1 of IS: 800 – 1984)

P(DL+LL+WL) = 45 + 40 + 30 = 115T

A =142.46 cm2; ryy = 4.40 cm. L = 5.0M

The permissible stress is increased as per clause 3.9.2

Percentage Strength attained = i.e. section is safe

(b) Design by LSM (Clause 7.1.2 of draft IS: 800)

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P(DL+LL+WL) = 138.0T (Factored load)

Flange of ISMB400 - 140 x 16; Web – 340 x 8.9

(Refer: Table – 3.1 of code)

Entire section is effective in compression

Euler Buckling Stress ;

For minor axis buckling and tf <40mm Curve ‘c’ is effective (Refer: Table 7.2 of code)Non-dimensional slenderness ratio= =1.2788

= 0.49 corresponding to curve “c” as per table 7.1)

Stress Reduction Factor =

Design Stress= fcd = =0.398x250/1.10 =90.45 MPa =904.5 Kg/m2

Therefore, Pd = Ae.fcd =142.46 x 904.5 / 1000 =128.86 T < 138 T

Hence design compressive strength Pd is less than applied factored load)

Section fails in LSM but not in WSM

3.2.2 Example – 2: The same example is calculated with the following different set of loading.

DL = 60.0T; LL = 50.0T; WL = 30T

(a) WSM (Clause 5.1 of IS: 800 – 1984)

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Total Load = 140.0T

Try built up Flange - 220 x 25 thk.Web - 500 x 12 thk.

(Following the same procedure as in the previous problem)

A = 170 cm2, ryy = 5.11 cm, Ixx = 88359 cm4

; Percentage strength attained = 823/1097 = 0.75

Hence, Section is safe

(b) LSM (Clause 7.1.2 of draft code) -Governing Factored load =1.2(DL+LL+WL) = 60 x 1.2 + 50 x 1.2 + 30 x 1.2=168T

Ac = 170 cm2

Section is Plastic (Ref: table 3.1 of draft code)

Entire section is in compression

Euler Buckling Stress =

Since tf <40 mm curve ‘c’ has to be followedfcd = 1100 kg/cm2

Pd = 1100 x 170/1000 = 187.0T

Therefore section is safe.Percentage strength attained = 168/187= 0.898 > 0.75(for WSM)Hence, WSM is economical than LSM

4.0 LIMIT STATE METHOD VIS-À-VIS WORKING STRESS METHOD

The basic comparison between the two methods of design namely the Limit State Method (LSM) and the Working Stress Method (WSM) should be done keeping in mind mainly two factors, firstly, the economy aspect, which is most important from the view point of the country’s socio-economic background and secondly but no less important is the rationality of approach in design. Comparing the results obtained, it can be seen that in a tension member, LSM

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gives more economy than WSM. The same trend can be seen for flexure members, whereas, for members subjected to purely axial compressive force (compression members) WSM gives more economy than the LSM.

To make a more comprehensive study in order to get a better picture of the economy aspect while comparing LSM and WSM for various types of member (viz. tension, compression, flexure etc.) various values of loading and their combination should be considered to get a firm idea as to which method is more economical. Thus after carrying out various designs for all types of members under different loading conditions and load combinations, the designs are furnished in tabular form showing actual economy obtained in both type of designs. Table – 3a & Table – 3b contain series of designs of standard tension members with angles where Tables – 3a contains design inputs and Table – 3b gives the corresponding outputs both in WSM and LSM. Similarly Table – 4a & Table – 4b gives series of deigns for compression members and Table – 5a & Table – 5b gives series of flexure member deign. The designs have been done using mild steel section of grade Fe 410 conforming to IS: 2062 having Ultimate Strength 410 MPa (fu), yield strength of 250 MPa (fy), Young’s Modulus 2 x 105 MPa and partial safety factor for material of 1.10 (mo) as described earlier.

TENSION MEMBERS

Table – 3a (DESIGN INPUTS)

Sl. No

Section Type

Section Type

of End conn.

No. of

Bolts

Bolt Hole Dia

(mm)

Applied Load Load Factor (LSM) [T - M]

 

DL LL WL L Gauge Ag An Anc Ago

( T ) ( T ) ( T ) D+L D+L+W D+W (M) (mm) (cm2) (cm2) (cm2) (cm2)

1 ISA 50 6 Weld - - 3.00 2.50 2.50 5.50 6.02 4.14 5.00 28.00 5.68 5.68 2.84 2.842 ISA 50 6 Bolt 4 13.5 3.00 2.50 2.50 5.50 6.02 4.14 5.00 28.00 5.68 4.87 2.03 2.843 2ISA 50 6 Weld - - 6.00 4.00 2.50 10.00 9.40 6.39 5.00 28.00 11.36 11.36 5.68 5.684 2ISA 50 6 Bolt 4 13.5 6.00 4.00 2.50 10.00 9.40 6.39 5.00 28.00 11.36 9.74 4.06 5.685 ISA 50 6 Weld - - 3.00 3.00 3.50 6.00 7.14 6.50 5.00 28.00 5.68 5.68 2.84 2.846 ISA 50 6 Bolt 4 13.5 3.00 3.00   6.00     5.00 28.00 5.68 4.87 2.03 2.847 2ISA 50 6 Weld - - 6.50 6.50   13.00     5.00 28.00 11.36 11.36 5.68 5.688 2ISA 50 6 Bolt 6 17.5 6.50 6.50   13.00     5.00 28.00 11.36 9.26 3.58 5.689 ISA 75 6 Weld     4.50 4.50   9.00     5.00 40.00 8.66 8.66 4.33 4.3310 ISA 75 6 Bolt 6 22 4.50 4.50   9.00     5.00 40.00 8.66 7.34 3.01 4.33

Table – 3b (DESIGN OUTPUTS)

Sl. No.

WSM LSM

k Aeff T(actual) T(perm) % strength attained

bs lw b T(fact.) Tdg Tdn Tdb T(perm) % strength attained  (cm2) ( T ) ( T ) (mm) (mm)   ( T ) ( T ) ( T ) ( T ) ( T )

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1 0.75 4.97 8.00 9.92 80.68 50.00 114.30 1.173 9.60 12.91 15.95   12.91 74.372 0.68 3.97 8.00 7.91 101.09 78.00 223.50 1.219 9.60 12.91 13.86 13.737 12.91 74.373 0.83 10.41 12.50 20.77 60.17 50.00 178.59 1.254 15.00 25.82 32.96   25.82 58.104 0.78 8.50 12.50 16.95 73.73 78.00 223.50 1.219 15.00 25.82 27.72 27.475 25.82 58.105 0.75 4.97 9.50 9.92 95.81 50.00 135.73 1.208 11.40 12.91 16.18   12.91 88.316 0.68 3.97 6.00 5.95 100.84 78.00 223.50 1.219 9.00 12.91 13.86 13.737 12.91 69.727 0.83 10.41 13.00 15.62 83.23 50.00 185.73 1.260 19.50 25.82 33.03   25.82 75.538 0.76 7.89 13.00 11.84 109.82 78.00 367.50 1.290 19.50 25.82 27.22 49.745 25.82 75.539 0.75 7.58 9.00 11.37 79.18 75.00 128.58 1.097 13.50 19.68 23.57   19.68 68.5910 0.68 5.94 9.00 8.90 101.07 115.00 372.00 1.239 13.50 19.68 21.08 32.269 19.68 68.59

COMPRESSION MEMBERS

Table – 4a (DESIGN INPUTS)

Sl. No

Section

Design Parameters Applied Load Design Load (WSM) [T-M]

Design load

(WSM)

Design load

(LSM)L Ag rmin K Le Le/rmin fcc DL LL WL

(M) (cm2) (cm)   (M)   (N/mm2) ( T ) ( T ) ( T ) D+L D+L+W D+W ( T ) ( T )1 2ISA50x6 2.00 11.36 1.51 0.85 1.70 112.58 155.73 3.00 2.50 2.50 5.50 6.02 4.14 6.02 9.602 ISA50x6 1.50 5.68 0.96 0.85 1.28 132.81 111.91 1.25 0.75 1.50 2.00 2.63 2.75 2.75 4.203 2ISA50x6 2.00 11.36 1.51 0.85 1.70 112.58 155.73 4.00 3.00   7.00     7.00 10.504 ISA50x6 1.50 5.68 0.96 0.85 1.28 132.81 111.91 1.50 1.50   3.00     3.00 4.505 MB350 4.00 66.71 2.84 0.90 3.60 126.76 122.85 20.00 15.00 10.00 35.00 33.83 22.56 35.00 54.006 MB350 4.00 66.71 2.84 0.90 3.60 126.76 122.85 20.00 10.00   30.00     30.00 45.007 MC250 3.50 38.67 2.38 0.90 3.15 132.35 112.68 10.00 4.00 4.00 14.00 13.53 10.53 14.00 21.608 MC250 3.50 38.67 2.38 0.90 3.15 132.35 112.68 10.00 4.00   14.00     14.00 21.009 MC300 4.00 45.64 2.61 0.85 3.40 130.27 116.32 12.00 5.00 12.00 17.00 21.80 24.00 24.00 36.0010 MC300 4.00 45.64 2.61 0.85 3.40 130.27 116.32 12.00 12.00   24.00     24.00 36.00

Table – 4b (DESIGN OUTPUTS)

Sl. No.

WSM LSM

ac(perm) Pac(perm) % strength attained

Aeff Buckling Class

fcd Pd%

strength attained(N/mm2) ( T ) (Cm2)         (N/mm2) ( T )

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1 69.43 7.89 76.26 11.36 1.267 c 0.49 1.564 0.403 91.60 10.41 92.262 54.93 3.12 88.14 5.68 1.495 c 0.49 1.934 0.316 71.88 4.08 102.873 69.43 7.89 88.75 11.36 1.267 c 0.49 1.564 0.403 91.60 10.41 100.904 54.93 3.12 96.15 5.68 1.495 c 0.49 1.934 0.316 71.88 4.08 110.225 58.87 39.27 89.12 66.71 1.427 b 0.34 1.726 0.371 84.25 56.20 96.086 58.87 39.27 76.39 66.71 1.427 b 0.34 1.726 0.371 84.25 56.20 80.077 55.22 21.35 65.56 38.67 1.489 c 0.49 1.925 0.318 72.26 27.94 77.308 55.22 21.35 65.56 38.67 1.489 c 0.49 1.925 0.318 72.26 27.94 75.159 56.55 25.81 92.99 45.64 1.466 c 0.49 1.885 0.326 74.05 33.79 106.5310 56.55 25.81 92.99 45.64 1.466 c 0.49 1.885 0.326 74.05 33.79 106.53

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5.0 CONCLUSIONS

The trends giving the comparative economy between WSM and LSM have been represented by means of graphical diagrams as shown in figure 1, 2 and 3. Figure – 1 represents the comparison between the percentage of design strength of a member utilized in WSM design with the corresponding percentage in LSM design for tension members for all the design options as done in Table – 3a & 3b. Similarly the same comparisons for compression and flexure members have been represented by figure – 2 and 3 respectively.

Fig – 1 Percentage strength utilized in Tension Members

0.0020.0040.0060.0080.00100.00120.00

1 2 3 4 5 6 7 8 9 10

Various Design Options

Per

cen

tag

e S

tren

gth

U

tili

sed

WSM

LSM

0.0020.0040.0060.0080.00100.00120.00

1 2 3 4 5 6 7 8 9 10

Various Design Options

Per

cen

tag

e S

tren

gth

U

tili

sed

WSM

LSM

Fig – 2 Percentage strength utilized in Compression Members

0.00020.00040.00060.00080.000100.000120.000

1 2 3 4 5 6 7 8 9 10

Various Design Options

Per

cen

tag

e S

tren

gth

U

tili

sed

WSM

LSM

Fig – 3 Percentage strength utilized in Members subjected to Flexure

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As have been stated earlier it is clear from the above figure that LSM design gives more economy than WSM design for tension and flexure members but WSM gives more economy in compression members. The individual reasonings that can be established for these phenomena are mainly as follows:

1. Tension members: In tension members the margin of economy in LSM is considerable. Though, there is partial benefit in WSM over LSM for DL+LL+WL condition due to the increase of 33% considered in permissible stress in WSM, the rational LSM method not only gives equal weightage to yielding of the gross section, but also to rupturing of the net section and the block shear failure at the connection.

Both in WSM and LSM reduction in area is done due to shear lag effect, but in WSM the stress is allowed to reach up to yield strength both in the connected element and the outstanding element of a member under any design condition. According to LSM, permissible stress in the connected element is allowed to go up to the ultimate strength of the material and that of the outstanding member up to the yield strength. When the gross area is considered for yielding, the yield strength is considered for the entire cross section of the member in LSM, which is not allowed in WSM.

2. Compression Members: The WSM method gives a better result as is evident from Fig – 2. To discuss the major reasons behind this, Fig 7.1 of draft IS: 800 (LSM version) must be refered to, which gives various column buckling curves and Table 7.2 which gives, the actual curve to be adopted for a particular type of section (viz. Rolled – I, Welded – I, Channel, SHS, RHS, Angles, Tees etc) undergoing buckling about a particular axis.

It is clear from the curves in Fig 7.1, that curve ‘a’ gives the maximum fcd (hence the maximum Pd or permissible load) value and the coefficient gradually reduces in curves ‘b’, ‘c’ and ‘d’. From Table 7.2 of draft code it can be seen that for minor axis buckling of Welded – I, Rolled Channel, Angles and Double-angles, curve ‘c’ is followed for design, and only for Rolled – I with flange thickness less than 40 mm and h/b less than 1.2 curve ‘b’ is adopted. For major axis buckling in Rolled – I and Welded – I section curve ‘a’ and ‘b’ respectively may be adopted, whereas WSM considers only curve ‘b’ for any design of compression member. Thus, for major axis buckling of I - section, LSM will give better result than WSM since curve ‘a’ is used in LSM and ‘b’ in WSM. Therefore, economical design may be achieved by making the structural arrangements such that the slenderness ratio about the major axis is the design criteria for a compression member of I - section. Otherwise in practice WSM will always give more economy.

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