Proceedings of 0th Indian Engineering Congress, the 1st

Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway, December 2015, pp. 163-171

Valuation of Strength of Structural Steel Angle Sections, under IS Code: 800 - 1984 – A Case Study with Equal vis-a-vis Unequal Angles

Manoj Kumar Varshaney and Nivesh Kumar Varshney
1Civil Engineering, D. N. Polytechnic, Meerut (U.P.) 250103, India; [email protected]
2Civil Engineering, Uttaranchal University, Dehradun (Uttarakhand), India; [email protected]

1. Introduction
Basically the structural steel is an alloy of iron, carbon-n-little parts of manganese, chrome nickel, sulfur, phosphorous-n-copper to form its rolled steel sections like angles, tees, channels, girders-n-plates which are used as beams, truss frames, columnbases, plate-girders etc to bear loads in the module of tensile-n-compressive stresses to safe the structure in deflection-n- bending. Structural steel is weather resistant and more stress bearing than normal steel. As normal specified steel is used in utensils, toys, vehicle-frames, furniture-n-watches etc., where loads and incoming varying stresses are not of structural type. While designing the steel structure two codes are usually followed viz. IS-Code: 800-1984 and Code 800-2000 which are known as elastic method and limit state method respectively.
Elastic method is simple-n-easy to design the structure, wherein stress-strain relation is considered linear till yield stress. The permissible stress is kept by dividing it by factor of safety. Factor of safety is the failure load divided by working load. But it is not

true for the material. As the material can resist load after the yield appear on the fiber of steel. Hence the section becomes uneconomical.
In limit state working load is taken into account by multiplying the factor 1.5 to strengthen n serviceability of structure. The limitable strength is desired to avoid the collapse of the structure n safe the life. The permissible stresses are taken much higher than working stresses. In working stress, stresses are taken like ft=150N/mm2, while ft=227 N/ mm2-n-rupture stress 295N/mm2, are taken in limit state. Though the paper theme has no concern with design differentiation, however it is seem necessary to go to narrow analogous to the stresses in respective methods of design.
2. General Concept
So far the title of the paper is concern wherein the study has been made for angles of equal and unequal in size but having same cross sectional area, have been used as tension and compression members and their ends have either single riveted or double riveted.

* Author for correspondence

Valuation of Strength of Structural.....

The strength has been calculated by using various conditional formulas and higher strength bearing condition under IS Code 800-1984, is recommended to use at construction sites where steel structures are being erected.
To make it lucid and easy & to make understandable the title to the readers it becomes necessary to illustrate by setting an example for choosing angle ISA-200*100*15 mm and ISA150*150*15 mm having cross sectional area 4278 mm2 are attached with 20mm thick gusset plate for its long leg /short leg jointed by 20mm diameter rivet shank. The permissible stress in tension has been taken 150 N/mm2 for Fe-250 grade steel and corresponding stresses in compression have been taken from standard table by interpolation. It has been assumed that compression member is of discontinuous type.
3. Methodology as Tension Member
The angle members of truss are either single or double, used as tension member either side to gusset plate or one side to gusset plate. Which connection will give higher strength, either long leg connected or short leg connected to gusset plate of angle, will be treated as best in economical design for valuation.

3.1 Case Study 1: Single Angle with Gusset Plate as Tension Member Riveted with 20mm Rivet Diameter
3.1.1 Connected Leg Area=(150-21.5-7.5) 15=1815 mm2
outstanding area=(150-7.5) 15 =2137.5 mm2 K=0.72 ANET = 3354 mm2 Ft=503100N
3.1.2 Unequal Angle
200*100*15mm whose long leg connected to 20mm thick gusset plate.
connected area=(200-21.5-7.5) 15=2565 mm2 outstanding area=(100-7.5) 15=1387.5 mm2 K=0.85 Anet=3744.375 mm2 Ft=561656N

Table 1. Comparative Study Table as tension single member

Sl.No

Angle

Leg connected Connection

1

Equal ISA-150 150 15

Any leg

single riveted

2

Unequal ISA 200 100 15

long leg

single riveted

3

Unequal ISA 200 100 15 short leg

single riveted

Tensile strength 503100 N 561656 N
387260.79 N

Preference 2nd 1st 3rd

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Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway

Manoj Kumar Varshaney and Nivesh Kumar Varshney

3.1.3 Unequal Angle
200*100*15mm whose short leg is connected with 20mm thick gusset plate.
connected area=(100-21.5-7.5) 15=1065 mm2 outstanding area=(200-7.5) 15= 2887.5 mm2 K=0.52 Anet= 2581.74 mm2 Ft=387260.79 N
3.2 Comparative Study Table as Tension Single Member
Result-single unequal angle’s long leg connected to the gusset plate is showing higher strength than equal angle, whose tensile strength Ft=561656 N

3.3.1.2 Equal Angles are One Side to the 20 mm Thick Gusset Plate without Tacking Rivet
connected area=2(150-21.5-7.5) 15= 3630 mm2 outstanding area=2(150-7.5) 15=4275 mm2 K=0.72 Anet= 3630 +0.72(4275)=6708 mm2 Ft=6708(150)= 1006200 N Ft=1006200 N

3.3 Two Angle as Tension Member
Somewhere when load is more then to restrict the stress in the tension member two members of same dimensions are used. The two angle members are connected either side or only one side to the gusset plate.
3.3.1 Case Study 2: ISA 150*150*15mm and ISA 200*100*15mm
3.3.1.1 Equal Angles Either Side Connected with 20mm Thick Gusset Plate Means the Plate is Sandwiched Between Two Angles
Anet=(4278-43) 15= 3633 mm2 Ft= (3633)150 N Ft=544950 N

3.3.1.3 Equal Angles are One Side to 20mm Thick Gusset Plate with Tacking Rivet
Connected area= 3630 mm2 outstanding area=4275 mm2 Anet= 3630 +0.81(4275)=7092.75 mm2 Ft= 7092.75( 150)=1063912.5 N Ft=1063912.5 N

Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway 165

Valuation of Strength of Structural.....

3.3.1.4 Unequal Angles Short Leg is Connected with 20mm Thick Gusset Plate on its Either Side
Anet=3633mm2 Ft= (3633) 150= 544950 N Ft=544950N
3.3.1.5 Unequal Angles Short Leg is Connected with 20mm Thick Gusset Plate on its One Side without Tacking Rivet
Connected area= 2(100-21.5-7.5) 15= 2130 mm2 outstanding area= 2(200-7.5) 15= 5775 mm2 K=0.52 Anet= 2130 + 0.52(5775) =5133 mm2 Ft= 5133 (150)= 769950 N Ft=769950 N
3.3.1.6 Unequal Angles Short Leg is Connected with 20mm Thick Gusset Plate on its One Side with Tacking Rivet
Connected area= 2130 mm2 outstanding area= 5775 mm2 K=0.65 Anet= 2130+0.65(5775)= 5883.75 mm2 Ft= 5883.75 (150) =882562.5 mm2 Ft=882562.5 N

3.3.1.7 Unequal Angles Long Leg is Connected with 20mm Thick Gusset Plate on its Either Side
Anet= 3633 mm2 Ft= 3633 (150)= 544950 Ft=544950 N
3.3.1.8 Unequal Angles Long Leg is Connected with 20mm Thick Gusset Plate on its One Side without Tacking Rivet
Connected area=2(200-21.5-7.5) 15= 5130 mm2 Outstanding area= 2(100-7.5) 15=2775 mm2 K=0.85 Anet= 5130 +0.85 (2775)= 7488.75 mm2 Ft= 7448.75 (150)= 1123312.5 N Ft=1123312.5 N

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Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway

Manoj Kumar Varshaney and Nivesh Kumar Varshney

3.3.1.9 Unequal Angles Long Leg is Connected with 20mm Thick Gusset Plate on its One Side with Tacking Rivet
Connected area=2(200-21.5-7.5)15=5130 mm2 outstanding area=2(100-7.5)15=2775mm2 K=0.90 Anet= 5130+0.90(2775)=7627.5 mm2 Ft=7627.5 (150)=1144125 N Ft=1144125N

rivet is giving higher strength in tension whose Ft=1144125N (Table 2).
3.5 Discontinuous Compression Member
The members are either single equal or un-equal and double equal single or unequal and their legs are connected with 20mm thick gusset plate on various conditions with ends rivet either single riveted or double riveted with a length of 2000mm have been assumed and illustrated to get the result, for the theme of the paper.

3.4 Comparative Table for Tensile Strength of Two Angles Connected with 20mm Thick Gusset Plate on its Various Positions
Result- Double unequal angles long leg connected with one side of gusset plate without tacking

3.5.1 Equal Single Member Connected to the Gusset Plate with Ends Single Riveted
rvv=29.2, l=2000mm, l/rvv =2000/29.2 =68.5 stress at l/rvv 68.5=113.5 N/mm2 Fc=4278(113.5)(0.8) =388442.4 N Fc=388442.4 N

Table 2. Comparative table for tensile strength of two angles connected with 20mm thick gusset plate on its various positions

Sl.No. Double Angle Condition to gusset plate Connection Tensile Strength Preference

1

ISA 150 150 15

Either side

Any Leg

544950N

Same

2

ISA 200 100 15

Either side

Long Leg

544950N

Same

3

ISA 200 100 15

Either side

Short Leg

544950N

Same

1

150 150 15

one side without tacking

Any Leg

1006200 N

2nd

2

200 100 15

one side without tacking

Long Leg

1123312 N

1st

3

200 100 15

one side without tacking Short Leg

769950 N

3rd

1

150 150 15

one side without tacking

Any Leg

1063912.5 N

2nd

2

200 100 15

one side without tacking

Long Leg

1144125 N

1st

3

200 100 15

one side without tacking Short Leg

882562 N

3rd

Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway 167

Valuation of Strength of Structural.....

3.5.2 Unequal Single Angle Any Leg is Connected with Gusset Plate with Ends Single Riveted
ryy=26.4, l=2000mm , l/ryy=2000/26.4 =75.75 stress at l/ryy75.75 =103.475 N/mm2 Fc= 4278(103.475)(0.8) =354132.8 N/mm2 Fc=354132.8 N

3.6 Discontinuous Compression Member Double Equal and Double Unequal
Result=Equal angle single with ends double riveted
is more strength full compression member than
unequal angle, whose Fc=529616.4N connected with gusset plate under various positions may be there and they are having different strength. The higher resulting strength will show the good valuated strength steel angle section.

3.5.3 Equal Angle Single with Ends Double Riveted

rvv=29.2, l=0.85(2000)=1700mm, l/rvv =58.2
stress at l/rvv 58.2 =123.8 N/mm2 Fc= 4278(123.8)= 529616.4 N/mm2
FC=529616.4 N

=1700/29.2

3.6.1 Equal Angles either Side of Gusset Plate with Single Riveted
l=2000mm, Ixx=2(8968000)=17936000mm4 Iyy=2(8968000) +2(4278)(52.6)2 =41608398.56 mm4 Imin=17936000mm4 rxx=45.8, l/rxx= 2000/45.8 =43.7 stress at l/rxx 43.7= 136.4 N/mm2 Fc=4278(136.4)(0.8)=466849.584N
Fc=466849.584 N

3.5.4 Unequal Single Angle any Leg Connected with Ends Double Riveted
ryy=26.4, l=1700mm, l/ryy =1700/26.4 =64.4 stress at l/ryy 64.4 = 117.6N /mm2 Fc=117.6(4278)=503092 .8 N Fc=503092.8 N

3.6.2 Equal Angles are One Side of Gusset Plate with Single Riveted
Things will be same as in 3.6-1 Fc=466849.584 N

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Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway

Manoj Kumar Varshaney and Nivesh Kumar Varshney

Table 3. Comparative table for single compression member

Sl.No. Angle Single Leg Connected End Condition Compressive Strength

1

150 150 15

Any Leg

single riveted

388442.4 N

2

200 100 15

Any Leg

single riveted

354132.8 N

3

150 150 15

Any Leg

single riveted

529616.4 N

4

200 100 15

Any Leg

single riveted

503092.8 N

Preferance 3rd 4th 1st 2nd

3.6.3 Equal Angles either Side to Gusset Plate, Ends Double Riveted
l=0.85(2000)=1700mm, rxx=45.8, l/rxx=1700/45.8=37, stress at l/rxx37 =141.8N/mm2 Fc=4278(141.8)=606620 N Fc=606620 N

Fc=2(4278)(133.4)=913096.32 N Fc=913096.32N

3.6.4 Equal Angles One Side to Gusset Plate, Ends Double Riveted
This will be same as in 3.6-3 Fc=606620 N

3.6.6 Unequal Angle Long Leg, Connected either Side to the Gusset Plate, Ends Double Riveted
l=1750mm, rmin=41.63 l/rmin =1750/41.63=40.83 or 40 stress at l/rmin 40=139 N/mm2 Fc=2(4278)(139)=1189284 N
Fc=1189284 N

3.6.5 Unequal Angle Long Leg, Connected either Side to the Gusset Plate, Ends Single Riveted

Ixx=2(17500000)=35000000 mm4 Iyy=2(2981000) +2(4278)(32.2)2 Imin.=14833203 mm4
rmin=41.63
l/rmin=2000/41.63 =48 stress al l/rmin48=133.4 N/mm2

=14833203 mm4

3.6.7 Unequal Angles Short Leg Connected either Side to Gusset Plate Ends Single Riveted
lxx=2(2981000)=5962000 mm4 Iyy=2(17500000)+2(4278)(81.8)2=92250249.44
mm4 Imin=5962000mm4 rmin=26.4 l/rmin=2000/26.4=75.75

Proceedings of 30th Indian Engineering Congress, the 21st Century Engineering: The Make in India Pathway 169

Valuation of Strength of Structural.....

Table 4. Comparative table for double angles as compression member under various positions

Sl.no. Double

Leg

End

Gusset plate Condition Compressive- Preference

Angle Connected Condition

strength

1

150 150 15 Any Leg single riveted Angle either side of plate 466849.6 N

8th

2

150 150 15 Any Leg single riveted Angle one side of plate 466849.6 N

8th

3

150 150 15 Any Leg Double riveted Angle one side of plate 597208.8 N

7th

4

150 150 15 Any Leg Double riveted Angle either side of plate 597208.8 N

7th

5

200 100 15 Long Leg single riveted Angle either side of plate 913096.3 N

4th

6

200 100 15 Long Leg Double riveted Angle either side of plate 1189284 N

1st

7

200 100 15 Short Leg single riveted Angle either side of plate 904555.3 N

5th

8

200 100 15 Long Leg single riveted Angle one side of plate 904555.3 N

5th

9

200 100 15 Long Leg Double riveted Angle one side of plate 999600 N

3rd

10 200 100 15 Short Leg Double riveted Angle either side of plate 999600 N

3rd

11 200 100 15 Short Leg single riveted Angle one side of plate 848160 N

6th

12 200 100 15 Short Leg Double riveted Angle either side of plate 1132875 N

2nd

stress for l/rmin 75.75=105.675 N/mm2 Fc=2(4278)(105.675)=904155.3N
Fc=904155.3 N

3.6.9 Unequal Angles Long Leg Connected One Side to the Gusset Plate Ends Double Riveted
l=1700 mm, rmin=26.4, l/rmin=1700/26.4=64.4 stress at l/rmin64.4=117.6N/mm2 Fc=2(4278)(117.6)=1006185 N Fc=1006185N

3.6.8 Unequal Angles Long Leg Connected One Side to the Gusset Plate, Ends Single Riveted
The strength will be same as in 3.6-7 Fc=904155.3 N

3.6.10 Unequal Angles Short Leg Connected either Side to the Gusset Plate Ends Double Riveted
Fc=999600N

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Manoj Kumar Varshaney and Nivesh Kumar Varshney

3.6.11 Unequal Angles Short Leg one Side to Gusset Plate Ends Single Riveted
Ixx=35000000mm4 Iyy=1017782mm4 rmin=34.5, l/rmin=2000/34.5=58 stress at l/rmin 58=124N/mm2 Fc=2(4278)(124)=848160 Fc=848160 N
3.6.12 Unequal Angles Short Leg either Side of Gusset Plate, Ends Double Riveted
Fc=1132875 N
4. Result and Discussions
The study reveals that the angles bearing same crosssectional area of either equal or unequal angles, whether they are single or double, while using as tension member, unequal angles-long leg connected with gusset plate will show higher strength. Long leg connected one side to gusset plate with tacking rivet as tension member has shown highest strength than other conditions while using double angles

So far the compression member is concerned, single equal angle has shown good strength with ends double riveted, than unequal angle. If double angles are used then unequal angles long leg connection, either side to gusset plate, with ends double riveting has been showing the highest compressive strength than only side connection to gusset plate even equal angles.
Hence it is finally discussed with this paper and recommended to use single unequal angle with its long leg connected to gusset plate and using it as tension member is preferable rather than equal angle rather than unequal short leg connected as constrain. Also if double angles are being used as tension member then unequal angles long leg connected to gusset plate to its one side with tacking rivet will be showing highest tensile strength than without tacking rivet. If constrain then equal angles one side to gusset plate plus tacking rivet and then without tacking rivet may be used. Short leg connection is not recommended to use in structures.
As compression member single equal angle with ends double riveted is recommended to use in place of unequal angle. It is too recommended that if double angles are being used as compression member than long leg connected either side to gusset plate is having highest strength rather than one side to gusset plate of long leg connected. Equal angles are not recommended to use as compression member.
5. Reference
1. Varshaney MK. Book design of steel and masonry structures.

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