Chapter 14Design of Members Subjected to Bending

NBC 2016 (SP 7:2016) Volume 1

2016 · PDF page 1006

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14.1 General

Members subjected to predominant bending shall have adequate design strength to resist bending moment, shear force, and concentrated forces imposed upon and their combinations. Further, the members shall satisfy

the deflection limitation presented in Section 6(e), as serviceability criteria. Member subjected to other forces in addition to bending or biaxial bending shall be designed in accordance with Section 6(j).

14.1.1 Effective Span of Beams

The effective span of a beam shall be taken as the distance between the centres of the supports, except where the point of application of the reaction is taken as eccentric at the support, when it shall be permissible to take the effective span as the length between the assumed lines of the reactions.

14.2Design Strength in Bending (Flexure)

The design bending strength of beam, adequately supported against lateral torsional buckling (laterally supported beam) is governed by the yield stress (see 14.2.1). When a beam is not adequately supported against lateral buckling (laterally un-supported beams) the design bending strength may be governed by lateral torsional buckling strength (see 14.2.2).

The factored design moment, $M$ at any section, in a beam due to external actions, shall satisfy

M \leq M _ {\mathrm{d}}

where

$M_{\mathrm{d}} =$ design bending strength of the section, calculated as given in 14.2.1.2.

14.2.1 Laterally Supported Beam

A beam may be assumed to be adequately supported at the supports, provided the compression flange has full lateral restraint and nominal torsional restraint at supports supplied by web cleats, partial depth end plates, fin plates or continuity with the adjacent span. Full lateral restraint to compression flange may be assumed to exist if the frictional or other positive restraint of a floor connection to the compression flange of the member is capable of resisting a lateral force not less than 2.5 percent of the maximum force in the compression flange of the member. This may be considered to be uniformly distributed along the flange, provided gravity loads constitute the dominant loading on the member and the floor construction is capable of resisting this lateral force.

The design bending strength of a section which are not susceptible to web buckling under shear before yielding (where $d / t_{\mathrm{w}} \leq 67e$ ) shall be determined according to 14.2.1.2.

14.2.1.1 Section with webs susceptible to shear buckling before yielding

When the flanges are plastic, compact or semi-compact but the web is susceptible to shear buckling before

yielding (see 14.4.2.1), the design bending strength shall be calculated using one of the following methods:

a) The bending moment and axial force acting on the section may be assumed to be resisted by flanges only and the web is designed only to resist shear (see 14.4).

b) The bending moment and axial force acting on the section may be assumed to be resisted by the whole section. In such a case, the web shall be designed for combined shear and normal stresses using simple elastic theory in case of semi-compact webs and simple plastic theory in the case of compact and plastic webs.

14.2.1.2 When the factored design shear force does not exceed $0.6 V_{d}$ , where $V_{d}$ is the design shear strength of the cross-section (see 14.4), the design bending strength, $M_{d}$ shall be taken as:

M_{\mathrm{d}} = \beta_{\mathrm{b}}Z_{\mathrm{p}}f_{\mathrm{y}} / \gamma_{\mathrm{m0}}

To avoid irreversible deformation under serviceability loads, $M_{d}$ shall be less than $1.2 Z_{e} f_{y} / \gamma_{m0}$ in case of simply supported and $1.5 Z_{e} f_{y} / \gamma_{m0}$ in case of cantilever beams;

where

\beta_ {\mathrm{b}} \quad = 1. 0 \text {for plastic and compact sections};

= Z _ {\mathrm{e}} / Z _ {\mathrm{p}} \text {for semi - compact sections;}

$Z_{p}, Z_{e} = \text{plastic and elastic section moduli of the cross-section, respectively};$

$f_{\mathrm{y}} =$ yield stress of the material; and

\gamma_ {\mathrm{m} 0} \quad = \text {partial safety factor (see 11.4.1).}

14.2.1.3 When the design shear force (factored), $V$ exceeds $0.6V_{\mathrm{d}}$ , where $V_{\mathrm{d}}$ is the design shear strength of the cross-section (see 14.4) the design bending strength, $M_{\mathrm{d}}$ shall be taken as:

M _ {\mathrm{d}} = M _ {\mathrm{dv}}

where

$M_{dv} =$ design bending strength under high shear as defined in 15.2.

14.2.1.4 Holes in the tension zone

a) The effect of holes in the tension flange, on the design bending strength need not be considered if

(A _ {\mathrm{nf}} / A _ {\mathrm{gf}}) \geq (f _ {s} / f _ {\mathrm{u}}) (\gamma_ {\mathrm{m1}} / \gamma_ {\mathrm{m0}}) / 0. 9

where

$A_{nf}/A_{gf}$ = ratio of net to gross area of the flange in tension;

$f_{y}/f_{u}$ = ratio of yield and ultimate stress of the material; and

$\gamma_{\mathrm{ml}} / \gamma_{\mathrm{m0}} =$ ratio of partial safety factors

against ultimate to yield stress (see 11.4.1).

When the $A_{nf}/A_{gf}$ does not satisfy the above requirement, the reduced effective flange area, $A_{ef}$ satisfying the above equation may be taken as the effective flange area in tension, instead of $A_{gf}$ .

b) The effect of holes in the tension region of the web on the design flexural strength need not be considered, if the limit given in 14.2.1.4(a) above is satisfied for the complete tension zone of the cross-section, comprising the tension flange and tension region of the web.

c) Fastener holes in the compression zone of the cross-section need not be considered in design bending strength calculation, except for oversize and slotted holes or holes without any fastener.

14.2.1.5 Shear lag effects

The shear lag effects in flanges may be disregarded provided:

a) For outstand elements (supported along one edge), $b_{\mathrm{o}} \leq L_{\mathrm{o}} / 20$ ; and

b) For internal elements (supported along two edges), $b_{\mathrm{i}} \leq L_{\mathrm{o}} / 10$ .

where

$L_{\mathrm{o}} =$ length between points of zero moment (inflection) in the span,

$b_{\mathrm{o}} =$ width of the flange with outstand, and

$b_{i}$ = width of the flange as an internal element

Where these limits are exceeded, the effective width of flange for design strength may be calculated using specialist literature, or conservatively taken as the value satisfying the limit given above.

14.2.2Laterally Unsupported Beams

Resistance to lateral torsional buckling need not be checked separately (member may be treated as laterally supported, see 14.2.1) in the following cases:

a) Bending is about the minor axis of the section,

b) Section is hollow (rectangular/ tubular) or solid bars, and

c) In case of major axis bending, $\lambda_{\mathrm{LT}}$ (as defined herein) is less than 0.4.

The design bending strength of laterally unsupported beam as governed by lateral torsional buckling is given by:

M_{\mathrm{d}} = \beta_{\mathrm{b}}Z_{\mathrm{p}}f_{\mathrm{bd}}

where

$\beta_{\mathrm{b}} = 1.0$ for plastic and compact sections;

$= Z_{\mathrm{e}} / Z_{\mathrm{p}}$ for semi-compact sections;

$Z_{p}, Z_{e}=$ plastic section modulus and elastic section modulus with respect to extreme compression fibre;

$f_{bd}$ = design bending compressive stress, obtained as given below [see Tables 13(a) and 13(b)];

\begin{array}{r l r} {f _ {\mathrm{bd}}} & {=} & {c _ {\mathrm{LT}, \mathrm{y}} / \gamma_ {\mathrm{m0}; \mathrm{and}}} \end{array}

$\chi_{LT} =$ bending stress reduction factor to account for lateral torsional buckling, given by:

\chi_ {\mathrm{LT}} = \frac {1}{\left\{\phi_ {\mathrm{LT}} + \left[ \phi_ {\mathrm{LT}} ^ {2} - \lambda_ {\mathrm{LT}} ^ {2} \right] ^ {0 . 5} \right\}} \leq 1. 0

\phi_ {\mathrm{LT}} = 0. 5 \left[ 1 + \alpha_ {\mathrm{LT}} \left(\lambda_ {\mathrm{LT}} - 0. 2\right) + \lambda_ {\mathrm{LT}} ^ {2} \right]

$\alpha_{\mathrm{LT}}$ , the imperfection parameter is given by:

$\alpha_{\mathrm{LT}} = 0.21$ for rolled steel section

$\alpha_{\mathrm{LT}} = 0.49$ for welded steel section

The non-dimensional slenderness ratio, $l_{\mathrm{LT}}$ , is given by:

\begin{array}{r l} \lambda_ {\mathrm{LT}} & = \sqrt {\beta_ {\mathrm{b}} Z _ {\mathrm{p}} f _ {\mathrm{y}} / M _ {\mathrm{cr}}} \leq \sqrt {1 . 2 Z _ {\mathrm{e}} f _ {\mathrm{y}} / M _ {\mathrm{cr}}} \\ & = \sqrt {\frac {f _ {\mathrm{y}}}{/ f _ {\mathrm{cr,b}}}} \end{array}

where

$M_{cr}$ = elastic critical moment calculated in accordance with 14.2.2.1, and

$f_{cr,b}$ = extreme fibre bending compressive stress corresponding to elastic lateral buckling moment (see 14.2.2.1 and Table 14).

14.2.2.1 Elastic lateral torsional buckling moment

In case of simply supported, prismatic members with symmetric cross-section, the elastic lateral buckling moment, $M_{cr}$ , can be determined from:

M _ {\mathrm{cr}} = \sqrt {\left\{\left(\frac {\pi^ {2} E I _ {\mathrm{y}}}{\left(L _ {\mathrm{LT}}\right) ^ {2}}\right) \left[ G I _ {\mathrm{t}} + \frac {\pi^ {2} E I _ {\mathrm{w}}}{\left(L _ {\mathrm{LT}}\right) ^ {2}} \right] \right\}} = \beta_ {\mathrm{b}} Z _ {\mathrm{p}} f _ {\mathrm{cr}, \mathrm{b}}

$f_{cr,b}$ of non-slender rolled steel sections in the above equation may be approximately calculated from the values given in the Table 14, which has been prepared using the following equation:

f _ {\mathrm{cr,b}} = \frac {1 . 1 \pi^ {2} E}{(L _ {\mathrm{LT}} / r _ {\mathrm{y}}) ^ {2}} \left[ 1 + \frac {1}{2 0} \left(\frac {L _ {\mathrm{LT}} / r _ {\mathrm{y}}}{h _ {\mathrm{f}} / t _ {\mathrm{f}}}\right) ^ {2} \right] ^ {0. 5}

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

$f_{crb}$	$f_y$
$f_{crb}$	200	210	220	230	240	250	260	280	300	320	340	360	380	400	420	450	480	510	540
10 000	181.8	190.9	200	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
8 000	181.8	190.9	200	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
6 000	181.8	190.9	200	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
4 000	181.8	190.9	200	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
2 000	181.8	190.9	200	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
1 000	169.1	179.5	186	196.5	202.9	209.1	219.8	229.1	245.5	261.8	275.1	291.3	300.5	323.6	332.2	355.9	370.9	384.8	412.4
900	169.1	179.5	186	194.5	200.7	204.5	215.1	231.6	242.7	258.9	272	291.3	300.5	316.4	328.4	339.5	366.5	380.2	392.7
800	167.3	177.5	184	190.3	196.4	206.8	212.7	224	240	258.9	268.9	284.7	293.6	301.8	324.5	335.5	349.1	370.9	387.8
700	163.6	171.8	182	188.2	192	202.3	208	226.5	237.3	250.2	259.6	278.2	286.7	294.5	305.5	327.3	340.4	352.4	363.3
600	161.8	168	176	181.9	194.2	197.7	203.3	218.9	226.4	244.4	253.5	261.8	276.4	287.3	294	306.8	322.9	333.8	343.6
500	161.8	166.1	172	179.8	185.5	188.6	200.9	208.7	218.2	232.7	244.2	248.7	259.1	269.1	274.9	286.4	296.7	301.4	314.2
450	158.2	164.2	168	173.5	183.3	186.4	191.5	206.2	215.5	224	231.8	242.2	248.7	258.2	263.5	274.1	279.3	292.1	294.5
400	150.9	162.3	166	169.4	174.5	184.1	186.7	196	204.5	215.3	222.5	229.1	238.4	243.6	248.2	257.7	261.8	264.3	274.9
350	147.3	152.7	162	165.2	170.2	172.7	179.6	188.4	193.6	200.7	210.2	212.7	221.1	225.5	229.1	233.2	240	241.1	245.5
300	143.6	147	152	154.7	161.5	163.6	167.8	175.6	182.7	186.2	194.7	196.4	196.9	203.6	206.2	212.7	213.8	217.9	220.9
250	134.5	137.5	142	144.3	148.4	152.3	153.6	160.4	163.6	165.8	170	173.5	179.6	178.2	179.5	184.1	183.3	185.5	191.5
200	121.8	124.1	126	129.6	130.9	134.1	134.7	137.5	141.8	142.5	145.3	147.3	148.5	149.1	152.7	151.4	152.7	153	157.1
150	101.8	103.1	104	104.5	106.9	106.8	108.7	109.5	111.8	113.5	114.4	114.5	117.5	116.4	118.4	118.6	117.8	120.5	122.7
100	74.5	76.4	76	77.4	76.4	77.3	78	78.9	79.1	78.5	80.4	81.8	79.5	80	80.2	81.8	82.9	83.5	83.5
90	67.3	68.7	70	69	69.8	70.5	70.9	71.3	70.9	72.7	74.2	72	72.5	72.7	72.5	73.6	74.2	74.2	73.6
80	61.8	63	62	62.7	63.3	63.6	63.8	63.6	65.5	64	64.9	65.5	65.6	65.5	64.9	65.5	65.5	64.9	68.7
70	54.5	55.4	56	56.5	56.7	56.8	56.7	56	57.3	58.2	58.7	58.9	58.7	58.2	57.3	57.3	56.7	60.3	58.9
60	47.3	47.7	48	48.1	48	50	49.6	48.4	49.1	49.5	49.5	49.1	48.4	50.9	49.6	49.1	52.4	51	49.1
50	40	40.1	40	41.8	41.5	40.9	40.2	40.7	40.9	40.7	43.3	42.5	41.5	43.6	42	40.9	43.6	41.7	44.2
40	32.7	32.5	32	33.5	32.7	34.1	33.1	33.1	32.7	34.9	34	32.7	34.5	32.7	34.4	32.7	34.9	32.5	34.4
30	25.5	24.8	26	25.1	26.2	25	26	25.5	24.5	26.2	24.7	26.2	24.2	25.5	26.7	24.5	26.2	27.8	24.5
20	16.4	17.2	18	16.7	17.5	18.2	16.5	17.8	16.4	17.5	18.5	16.4	17.3	18.2	19.1	16.4	17.5	18.5	19.6
10	9.1	9.5	8	8.4	8.7	9.1	9.5	7.6	8.2	8.7	9.3	9.8	10.4	7.3	7.6	8.2	8.7	9.3	9.8

Table 13(b) Design Bending Compressive Stress Corresponding to Lateral Buckling, f_{\mathrm{bd}}, \alpha_{\mathrm{LT}} = 0.49 (Clause 14.2.2)

$f_{cr,b}$	$f_y$
$f_{cr,b}$	200	210	220	230	240	250	260	280	300	320	340	360	380	400	420	450	480	510	540
10 000	181.8	190.9	200.0	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
8 000	181.8	190.9	200.0	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
6 000	181.8	190.9	200.0	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
4 000	181.8	190.9	200.0	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
2 000	181.8	190.9	200.0	209.1	218.2	227.3	236.4	254.5	272.7	290.9	309.1	327.3	345.5	363.6	381.8	409.1	436.4	463.6	490.9
1 000	160.0	164.2	170.0	179.8	185.5	190.9	196.2	211.3	220.9	235.6	247.3	255.3	266.0	280	290.2	302.7	318.5	329.2	343.6
900	154.5	164.2	170.0	173.5	183.3	188.6	193.8	203.6	218.2	226.9	238.0	252.0	262.5	269.1	282.5	290.5	305.5	319.9	333.8
800	152.7	158.5	168.0	171.5	176.7	181.8	191.5	201.1	210.0	224.0	234.9	242.2	252.2	258.2	271.1	282.3	296.7	306	319.1
700	150.9	154.6	160.0	169.4	172.4	177.3	182.0	196	207.3	215.3	222.5	232.4	238.4	247.3	259.6	270	279.3	292.1	304.4
600	145.5	150.8	154.0	161.0	168.0	172.7	177.3	188.4	193.6	203.6	213.3	222.5	228	236.4	244.4	253.6	261.8	273.5	274.9
500	140.0	145.1	150.0	154.7	159.3	161.4	167.8	175.6	185.5	192	200.9	206.2	214.2	218.2	225.3	229.1	240	245.7	250.4
450	134.5	141.3	144.0	148.5	152.7	156.8	160.7	168	177.3	186.2	191.6	196.4	203.8	210.9	213.8	220.9	231.3	236.5	235.6
400	129.1	135.5	138.0	142.2	148.4	150	153.6	162.9	169.1	174.5	182.4	183.3	193.5	196.4	202.4	208.6	209.5	217.9	220.9
350	123.6	129.8	132.0	135.9	139.6	143.2	148.9	152.7	158.2	162.9	170	173.5	176.2	181.8	183.3	192.3	196.4	199.4	206.2
300	118.2	122.2	126.0	129.6	130.9	134.1	137.1	142.5	147.3	154.2	157.6	157.1	162.4	167.3	168	175.9	178.9	180.8	181.6
250	109.1	112.6	116.0	117.1	120.0	122.7	125.3	129.8	130.9	136.7	139.1	140.7	145.1	149.1	148.9	151.4	152.7	157.6	157.1
200	98.2	101.2	102.0	104.5	104.7	109.1	108.7	112	117.3	119.3	120.5	121.1	124.4	127.3	126	130.9	130.9	129.8	132.5
150	83.6	84.0	86.0	87.8	89.5	88.6	89.8	91.6	95.5	96.0	95.8	98.2	100.2	101.8	103.1	102.3	104.7	106.6	103.1
100	63.6	63.0	64.0	64.8	65.5	65.9	66.2	68.7	68.2	69.8	71.1	68.7	69.1	72.7	72.5	73.6	74.2	74.2	73.6
90	58.2	57.3	60.0	58.5	61.1	61.4	61.5	61.1	62.7	64.0	64.9	65.5	65.6	65.5	64.9	65.5	65.5	64.9	68.7
80	52.7	53.5	54.0	54.4	54.5	54.5	54.4	56	57.3	58.2	58.7	58.9	58.7	58.2	61.1	61.4	61.1	60.3	58.9
70	47.3	47.7	48.0	48.1	48.0	50.0	49.6	50.9	49.1	49.5	52.5	52.4	51.8	50.9	53.5	53.2	52.4	55.6	54.0
60	41.8	42.0	42.0	41.8	43.6	43.2	42.5	43.3	43.6	43.6	43.3	45.8	44.9	47.3	45.8	45.0	48.0	46.4	49.1
50	36.4	36.3	36.0	35.5	37.1	36.4	37.8	38.2	38.2	37.8	37.1	39.3	38.0	40.0	38.2	40.9	39.3	37.1	39.3
40	29.1	30.5	30.0	29.3	30.5	29.5	30.7	30.5	30.0	32.0	30.9	32.7	31.1	32.7	30.5	32.7	30.5	32.5	34.4
30	23.6	22.9	22.0	23.0	24.0	22.7	23.6	22.9	24.5	23.3	24.7	22.9	24.2	25.5	22.9	24.5	26.2	23.2	24.5
20	16.4	15.3	16.0	16.7	15.3	15.9	16.5	15.3	16.4	17.5	15.5	16.4	17.3	18.2	15.3	16.4	17.5	18.5	14.7
10	9.1	7.6	8.0	8.4	8.7	9.1	9.5	7.6	8.2	8.7	9.3	9.8	6.9	7.3	7.6	8.2	8.7	9.3	9.8

Table 14 Critical Stress, $f_{cr,b}$ (Clause 14.2.2.1)
$L_{LT}/r_y$	$h_t/t_f$
$L_{LT}/r_y$	8	10	12	14	16	18	20	25	30	35	40	50	60	80	100
10	22551.2	22255.1	22092.6	21994.1	21929.8	21885.7	21854.0	21805.4	21779.0	21763.1	21752.7	21740.5	21733.8	21727.2	21724.2
20	6220.5	5947.9	5794.5	5700.0	5637.8	5594.7	5563.8	5515.8	5489.7	5473.8	5463.5	5451.4	5444.8	5438.2	5435.1
30	3149.3	2905.9	2764.6	2676.0	2616.7	2575.3	2545.3	2498.5	2472.8	2457.1	2447.0	2434.9	2428.3	2421.7	2418.6
40	2036.1	1821.2	1693.0	1610.8	1555.1	1515.8	1487.0	1441.7	1416.5	1401.1	1391.0	1379.0	1372.5	1365.9	1362.8
50	1492.9	1303.2	1187.3	1111.8	1059.9	1022.7	995.3	951.7	927.1	912.0	902.0	890.2	883.7	877.1	874.2
60	1178.0	1009.5	905.0	835.6	787.4	752.4	726.4	684.6	660.9	646.1	636.4	624.7	618.2	611.7	608.7
70	973.9	823.2	728.5	664.8	620.1	587.4	562.9	522.9	500.0	485.5	476.0	464.4	458.0	451.7	448.7
80	831.3	695.4	609.2	550.7	509.1	478.4	455.3	417.2	395.1	381.2	371.8	360.5	354.1	347.7	344.7
90	725.9	602.6	523.6	469.5	430.9	402.2	380.4	344.2	322.9	309.3	300.2	289.1	282.8	276.5	273.5
100	644.7	532.0	459.3	409.3	373.2	346.4	325.8	291.4	270.9	257.7	248.8	237.9	231.8	225.5	222.5
110	580.4	476.6	409.3	362.9	329.2	303.9	284.5	251.8	232.1	219.3	210.8	200.1	194.0	187.8	184.8
120	527.9	431.9	369.5	326.0	294.5	270.7	252.3	221.2	202.4	190.1	181.6	171.2	165.2	159.1	156.2
130	484.3	395.0	336.8	296.1	266.5	244.1	226.7	197.1	179.0	167.1	158.8	148.6	142.8	136.7	133.9
140	447.6	364.2	309.5	271.5	243.4	222.3	205.8	177.5	160.2	148.7	140.7	130.8	125.0	119.0	116.2
150	416.0	337.8	286.6	250.6	224.2	204.2	188.4	161.5	144.8	133.7	126.0	116.3	110.6	104.7	101.9
160	388.7	315.2	266.8	232.8	207.8	188.8	173.9	148.2	132.0	121.3	113.9	104.3	98.8	93.0	90.1
170	364.9	295.4	249.6	217.5	193.7	175.6	161.4	136.7	121.3	111.0	103.6	94.4	89.0	83.2	80.4
180	343.9	278.0	234.6	204.1	181.5	164.2	150.6	127.1	112.2	102.2	95.2	86.0	80.7	75.0	72.3
190	325.2	262.6	221.3	192.3	170.7	154.2	141.2	118.6	104.3	94.6	87.8	79.0	73.7	68.1	65.3
200	308.3	248.8	209.6	181.7	161.2	145.4	133.0	111.3	97.5	88.1	81.4	72.8	67.8	62.2	59.5
210	293.3	236.5	198.9	172.4	152.7	137.6	125.7	104.8	91.5	82.4	75.9	67.5	62.6	57.1	54.5
220	279.5	225.3	189.3	163.9	145.1	130.6	119.1	99.0	86.2	77.4	71.2	62.9	58.1	52.7	50.1
230	267.1	215.2	180.7	156.3	138.2	124.3	113.3	93.9	81.5	72.9	66.9	58.9	54.1	48.8	46.2
240	255.8	205.8	172.8	149.4	132.0	118.6	108.0	89.3	77.2	69.0	63.1	55.3	50.6	45.4	42.8
250	245.3	197.3	165.6	143.0	126.3	113.4	103.2	85.1	73.5	65.5	59.7	52.1	47.5	42.4	39.8
260	235.7	189.5	159.0	137.3	121.1	108.7	98.8	81.3	70.1	62.3	56.7	49.3	44.8	39.7	37.2
270	226.8	182.3	152.8	131.9	116.3	104.3	94.7	77.9	67.0	59.4	53.9	46.8	42.2	37.3	34.8
280	218.6	175.7	147.2	126.9	111.9	100.2	91.1	74.7	64.1	56.8	51.5	44.4	40.0	35.2	32.7
290	210.9	169.4	141.9	122.3	107.8	96.6	87.7	71.8	61.5	54.3	49.2	42.2	38.1	33.2	30.8
300	203.8	163.7	137.1	118.1	104.1	93.2	84.5	69.1	59.1	52.1	47.1	40.4	36.2	31.5	29.0

The following simplified equation may be used in the case of prismatic members made of standard rolled I-sections and welded doubly symmetric I-sections, for calculating the elastic lateral buckling moment, $M_{cr}$ (see Table 14).

M _ {\mathrm{cr}} = \frac {\pi^ {2} E I _ {\mathrm{y}} h _ {\mathrm{f}}}{2 L _ {\mathrm{LT}} ^ {2}} \left[ 1 + \frac {1}{2 0} \left(\frac {L _ {\mathrm{LT}} / r _ {\mathrm{y}}}{h _ {\mathrm{f}} / t _ {\mathrm{f}}}\right) ^ {2} \right] ^ {0. 5}

where

$I_{\mathrm{t}}$ = torsional constant $\sum b_{\mathrm{i}}t_{\mathrm{i}}^{3} / 3$ for open section;

$I_{\mathrm{w}}$ = warping constant;

$I_{y}, r_{y} = \text{moment of inertia and radius of gyration, respectively about the weaker axis;}$

$L_{LT}$ = effective length for lateral torsional buckling (see 14.3);

$h_{\mathrm{f}}$ = centre-to-centre distance between flanges; and

$t_{\mathrm{f}}$ = thickness of the flange.

$M_{cr}$ for different beam sections, considering loading, support condition, and asymmetric section, shall be more accurately calculated using the method given in Annex D. The above equations for calculating $M_{cr}$ may be conservatively used for channel sections.

14.3Effective Length for Lateral Torsional Buckling

14.3.1 For simply supported beams and girders of span length, L, where no lateral restraint to the compression flanges is provided, but where each end of the beam is restrained against torsion, the effective length $L_{LT}$ of the lateral buckling to be used in 14.2.2.1 shall be taken as in Table 15.

In simply supported beams with intermediate lateral restraints against lateral torsional buckling, the effective length for lateral torsional buckling, $L_{\mathrm{LT}}$ to be used in 14.2.2.1, shall be taken as the length of the relevant segment in between the lateral restraints. In the case of intermediate partial lateral restraints, the effective length, $L_{\mathrm{LT}}$ shall be taken as equal to 1.2 times the length of the relevant segment in between the partial lateral restraints.

Restraint against torsional rotation at supports in these beams may be provided by,

a) web or flange cleats, or

b) bearing stiffeners acting in conjunction with the bearing of the beam, or

c) lateral end frames or external supports providing lateral restraint to the compression flanges at the ends, or

d) their being built into walls.

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

Sl No.	Conditions of Restraint at Supports		Loading Condition
Sl No.	Torsional restraint(2)	Warping Restraint(3)	Normal(4)	Destabilizing(5)
i)	Fully restrained	Both flangesfully restrained	0.70 L	0.85 L
ii)	Fully restrained	Only compressionflange fullyrestrained	0.75 L	0.90 L
iii)	Fully restrained	Both flangespartiallyrestrained	0.80 L	0.95 L
iv)	Fully restrained	Only compressionflange partiallyrestrained	0.85 L	1.00 L
v)	Fully restrained	No restraint in both flanges	1.00 L	1.20 L
vi)	Partially restrained by bottom flangesupport connection	No restraint in both flanges	1.0 L+2D	1.2 L+2D
vii)	Partially restrained bybottom flangebearing support	No restraint in both flanges	1.2 L+2D	1.4 L+2D
NOTES
1 Torsional restraint prevents rotation about the longitudinal axis.
2 Warping restraint prevents rotation of the flange in its plane.
3 D is the overall depth of the beam.
4 In case of continuous beams, L shall be taken as the distance between points of inflection, and the restraint conditions at the points of inflection should be considered.

14.3.2 For beams, which are provided with members giving effective lateral restraint to the compression flange at intervals along the span, in addition to the end torsional restraint required in 14.3.1, the effective length for lateral torsional buckling shall be taken as the distance, centre-to-centre of the restraint members in the relevant segment under normal loading condition and 1.2 times this distance, where the load is not acting on the beam at or above the shear centre and towards the shear centre, so as to have destabilizing effect during lateral torsional buckling deformation.

14.3.3 For cantilever beams of projecting length $L$ , the effective length $L_{\mathrm{LT}}$ to be used in 14.2.2.1 shall be taken as in Table 16 for different support conditions.

14.3.4 Where a member is provided intermediate lateral supports to improve the lateral buckling strength, these restraints should have sufficient strength and stiffness to prevent lateral movement of the compression flange at that point, relative to the end

14.3.5 Purlins adequately restrained by sheeting need not be normally checked for the restraining forces required by rafters, roof trusses or portal frames that carry predominately roof loads provided there is bracing of adequate stiffness in the plane of rafters or roof sheeting which is capable of acting as a stressed skin diaphragm.

14.3.6 In case of beams with double curvature bending, adequate direct lateral support to the compression flange in the hogging moment region may be provided as given above for simply supported beam. The effect of support to the tension (top) flange in the hogging moment region on lateral restraint to the compression flange may be considered as per specialist literature.

14.4Shear

The factored design shear force, $V$ , in a beam due to external actions shall satisfy

V \leq V _ {\mathrm{d}}

where

$V_{\mathrm{d}} =$ design strength

= V _ {\mathrm{n}} / \gamma_ {\mathrm{m0}}

where

$\gamma_{m0} = \text{partial safety factor against shear failure}$ (see 11.4.1).

The nominal shear strength of a cross-section, $V_{n}$ , may be governed by plastic shear resistance (see 14.4.1) or strength of the web as governed by shear buckling (see 14.4.2).

14.4.1 The nominal plastic shear resistance under pure shear is given by:

\left| V _ {\mathrm{n}} = V _ {\mathrm{p}} \right|

where

V _ {\mathrm{p}} = \frac {A _ {\mathrm{v}} f _ {\mathrm{yw}}}{\sqrt {3}}

$A_{\mathrm{v}} =$ shear area; and

$f_{\mathrm{yw}} =$ yield strength of the web.

14.4.1.1 The shear area may be calculated as given below:

a) I-and channel sections:

Major Axis Bending:

t _ {\mathrm{w}}

t _ {\mathrm{w}}

Minor Axis Bending:

Hot-rolled or welded : 2b $t_{f}$

b) Rectangular hollow sections of uniform thickness:

Loaded parallel to depth (h) : A h/(b+h) Loaded parallel to width (b) : A b/(b+h)

c) Circular hollow tubes of uniform : 2A/π thickness

d) Plates and solid bars : A where

$A =$ cross-section area,

b = overall breadth of tubular section, breadth of I-section flanges,

$d =$ clear depth of the web between flanges,

$h =$ overall depth of the section,

$t_\mathrm{f} =$ thickness of the flange, and

$t_\mathrm{w} =$ thickness of the web.

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

NOTE — Fastener holes need not be accounted for in plastic design shear strength calculation provided that:

A _ {\mathrm{vn}} \geq (f _ {\mathrm{j}} / f _ {\mathrm{u}}) (\gamma_ {\mathrm{mi}} / \gamma_ {\mathrm{nf0}}) A _ {\mathrm{v}} / 0. 9

If $A_{\mathrm{vn}}$ does not satisfy the above condition, the effective shear area may be taken as that satisfying the above limit. Block shear failure criteria may be verified at the end connections. Section 6(j) may be referred to for design strength under combined high shear and bending.

14.4.2 Resistance to Shear Buckling

14.4.2.1 Resistance to shear buckling shall be verified as specified, when

$d / t_{\mathrm{w}} > 67\varepsilon_{\mathrm{w}}$ for a web without stiffeners, and

> 6 7 \varepsilon_ {\mathrm{w}} \sqrt {\frac {K _ {\mathrm{v}}}{5 . 3 5}} \text {for a web with stiffeners}

where

$K_{\mathrm{v}} =$ shear buckling coefficient (see 14.4.2.2), and

\varepsilon_ {\mathrm{w}} = \sqrt {2 5 0 / f _ {\mathrm{yw}}}

14.4.2.2 Shear buckling design methods

The nominal shear strength, $V_{\mathrm{n}}$ , of webs with or without intermediate stiffeners as governed by buckling may be evaluated using one of the following methods:

a) Simple post-critical method — The simple post critical method, based on the shear buckling strength can be used for webs of I-section girders, with or without intermediate transverse stiffener, provided that the web has transverse stiffeners at the supports. The nominal shear strength is given by:

\left| V _ {\mathrm{n}} = V _ {\mathrm{cr}} \right|

where

$V_{cr} =$ shear force corresponding to web buckling

= A _ {\mathrm{v}} \tau_ {\mathrm{b}}

where

$\tau_{\mathrm{b}} =$ shear stress corresponding to web buckling, determined as follows:

when $\lambda_{\mathrm{w}} \leq 0.8$ , $\tau_{\mathrm{b}} = f_{\mathrm{yw}} / \sqrt{3}$
when $0.8 < \lambda_{w} < 1.2,$

\tau_ {\mathrm{b}} = \left[ 1 - 0. 8 \left(\lambda_ {\mathrm{w}} - 0. 8\right) \right] \left(f _ {\mathrm{yw}} / \sqrt {3}\right)

when $\lambda_{\mathrm{w}} \geq 1.2$ , $\tau_{\mathrm{b}} = f_{\mathrm{yw}} / \left( \sqrt{3} \lambda_{\mathrm{w}}^{2} \right)$

where

$\lambda_{\mathrm{w}} =$ Non-dimensional web slenderness ratio for shear buckling stress, given by:

\lambda_ {\mathrm{w}} = \sqrt {f _ {\mathrm{yw}} / (\sqrt {3} \tau_ {\mathrm{cr,e}})}

$t_{\mathrm{cr,e}} =$ elastic critical shear stress of the web

= \frac {K _ {\mathrm{v}} \pi^ {2} E}{1 2 \left(1 - \mu^ {2}\right) \left[ d / t _ {\mathrm{w}} \right] ^ {2}}

where

\mu = \text {Poisson's ratio, and}

$K_{v} = 5.35$ when transverse stiffeners are provided only at supports

= 4. 0 + 5. 3 5 / (c / d) ^ {2} \text {for} c / d < 1. 0

= 5. 3 5 + 4. 0 / (c / d) ^ {2} \text {for} c / d \geq 1. 0

where $c, d$ are the spacing of transverse stiffeners and depth of the web, respectively.

b) Tension field method — The tension field method, based on the post-shear buckling strength, may be used for webs with intermediate transverse stiffeners, in addition to the transverse stiffeners at supports, provided the panels adjacent to the panel under tension field action, or the end posts provide anchorage for the tension fields and if $c/d \geq 1.0$ , where c, d are the spacing of transverse stiffeners and depth of the web, respectively.

In the tension field method, the nominal shear resistance, $V_{\mathrm{n}}$ , is given by:

V _ {\mathrm{n}} = V _ {\mathrm{tf}}

where

V _ {\mathrm{tf}} = \left[ A _ {\mathrm{v}} \tau_ {\mathrm{b}} + 0. 9 w _ {\mathrm{tf}} t _ {\mathrm{w}} f _ {\mathrm{v}} \sin \phi \right] \leq V _ {\mathrm{p}}

where

$\tau_{\mathrm{b}} =$ shear stress corresponding to buckling of web 14.4.2.2(a);

$f_{\mathrm{v}} =$ yield strength of the tension field obtained

\text {from} \left[ f _ {\mathrm{yw}} ^ {2} - 3 \tau_ {\mathrm{b}} ^ {2} + \psi^ {2} \right] ^ {0. 5} - \psi ;

\psi = 1. 5 \tau_ {\mathrm{b}} \sin 2 \phi ;

$\phi =$ inclination of the tension field nearly

= \tan^ {- 1} \frac {\left(\frac {d}{c}\right)}{1 . 5};

$w_{\mathrm{tf}} =$ width of the tension field, given by:

= d \cos \phi - (c - s _ {\mathrm{c}} - s _ {\mathrm{t}}) \sin \phi ;

$f_{\mathrm{yw}} =$ yield stress of the web;

$d =$ depth of the web;

c = spacing of transverse stiffeners in the web; and

$s_{c}, s_{t}=$ anchorage lengths of tension field along the compression and tension flange, respectively, obtained from:

where

s = \frac {2}{\sin \phi} \left[ \frac {M _ {\mathrm{fr}}}{f _ {\mathrm{yw}} t _ {w}} \right] ^ {0. 5} \leq c

$M_{fr} =$ reduced plastic moment capacity of the respective flange plate (disregarding any edge stiffener) after accounting for the axial force, $N_{f}$ in the flange, due to overall bending and any external axial force in the cross-section, and is calculated as :

M _ {\mathrm{fr}} = 0. 2 5 b _ {\mathrm{f}} t _ {\mathrm{f}} ^ {2} f _ {\mathrm{yf}} \left[ 1 - \left\{N _ {\mathrm{f}} / \left(b _ {\mathrm{f}} t _ {\mathrm{f}} f _ {\mathrm{yf}} / \gamma_ {m 0}\right) \right\} ^ {2} \right] \Bigg |

where

$b_{f}, t_{f} = \text{width and thickness of the relevant flange, respectively; and}$

$f_{\mathrm{yf}} =$ yield stress of the flange.

14.5Stiffened Web Panels

14.5.1 End Panels Design (see Fig.12)

The girders in which the interior panel (panel A) is designed using tension field action, the end panels shall be designed using only simple post critical method, according to 14.4.2.2(a).

Additionally, the end panel along with the stiffeners should be checked as a beam spanning between the flanges to resist a shear force, $R_{\mathrm{tf}}$ , and a moment, $M_{\mathrm{tf}}$ , due to tension field forces as given in 14.5.3. Further, end stiffener should be capable of resisting the reaction plus a compressive force due to the moment, equal to $M_{\mathrm{tf}}$ [see Fig. (12)].

14.5.2 End Panels Designed Using Tension Field Action (see Fig. 13 and Fig. 14)

The end panel (Panel A) shall be designed according to 14.4.2.2(b).

Additionally it should be provided with an end post consisting of a single or double stiffener (see Fig. 13 and Fig. 14), satisfying the following.

a) Single stiffener (see Fig. 13) — The top of the end post should be rigidly connected to the flange using full strength welds.

The end post should be capable of resisting the reaction plus a moment from the anchor forces equal to $2/3 M_{\mathrm{tf}}$ due to tension field forces, where $M_{\mathrm{tf}}$ is obtained from 14.5.3. The width and thickness of the end post are not to exceed the width and thickness of the flange.

b) Double stiffener (see Fig. 14)— The end post should be checked as a beam spanning between the flanges of the girder and capable

Table 16Effective Length, L_{\mathrm{LT}} for Cantilever of Length, L (Clause 14.3.3)

Restraint Condition			Loading Conditions
At Support At top			Normal Destabilizing
(2)	(3)		(4)	(5)
a) Continuous, with lateral restraint to top flange	i) Freeii) Lateral restraint to top flangeiii) Torsional restraintiv) Lateral and torsional restraint		3.0L2.7L2.4L2.1L	7.5L7.5L4.5L3.6L
b) Continuous, with partial torsional restraint	i) Freeii) Lateral restraint to top flangeiii) Torsional restraintiv) Lateral and torsional restraint		2.0L1.8L1.6L1.4L	5.0L5.0L3.0L2.4L
c) Continuous, with lateral and torsional restraint	i) Freeii) Lateral restraint to top flangeiii) Torsional restraintiv) Lateral and torsional restraint		1.0L0.9L0.8L0.7L	2.5L2.5L1.5L1.2L
d) Restrained laterally, torsionally and against rotation on plan	i) Freeii) Lateral restraint to top flangeiii) Torsional restraintiv) Lateral and torsional restraint		0.8L0.7L0.6L0.5L	1.4L1.4L0.6L0.5L
Top restraint conditions
i) Free	ii) Lateral restraint to top flange	iii) Torsional restraint		iv) Lateral and torsional restraint

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

of resisting a shear force $R_{\mathrm{tf}}$ and a moment, $M_{\mathrm{tf}}$ due to the tension field forces as given in 14.5.3.

14.5.3 Anchor Forces

The resultant longitudinal shear, $R_{\mathrm{tf}}$ , and a moment $M_{\mathrm{tf}}$ from the anchor of tension field forces are evaluated as given below:

R _ {\mathrm{tf}} = \frac {H _ {\mathrm{q}}}{2} \text {and} M _ {\mathrm{tf}} = \frac {H _ {\mathrm{q}} d}{1 0}

where

H _ {\mathrm{q}} = 1. 2 5 V _ {\mathrm{p}} \left(1 - \frac {V _ {\mathrm{cr}}}{V _ {\mathrm{p}}}\right) ^ {1 / 2}

V _ {\mathrm{p}} = \frac {d t f _ {\mathrm{y}}}{\sqrt {3}}

d = \text {web depth},

If the actual factored shear force, $V$ in the panel designed using tension field approach is less than the shear strength, $V_{\mathrm{tf}}$ as given in 14.4.2.2(b), then the values of

$H_{\mathrm{q}}$ may be reduced by the ratio $\frac{V - V_{\mathrm{cr}}}{V_{\mathrm{tf}} - V_{\mathrm{cr}}}$

where

$V_{tf} =$ basic shear strength for the panel utilizing tension field action as given in 14.4.2.2(b), and

$V_{cr} =$ critical shear strength for the panel designed utilizing tension field action as given in 14.4.2.2(a).

FIG. 14 END PANEL DESIGNED USING TENSION FIELD ACTION (DOUBLE STIFFENER)

NOTES

1 Panel A is designed utilizing tension field action as given in 14.4.2.2(b).

2 Panel B is designed using simple post critical method as given in 14.4.2.2(a).

3 Bearing stiffener is designed for the compressive force due to bearing plus compressive force due to the moment $M_{tf}$ as given in 14.5.3.

FIG. 12 END PANEL DESIGNED NOT USING TENSION FIELD ACTION

NOTES

1 Panel A is designed utilizing tension field action as given in 14.4.2.2(b).

2 Bearing stiffener and end post is designed for combination of compressive loads due to bearing and a moment equal to $2/3\mathrm{M}_{\mathrm{tf}}$ as given in 14.5.3.

FIG. 13 END PANEL DESIGNED USING TENSION FIELD ACTION (SINGLE STIFFENER)

NOTES

1 Panel A is designed utilizing tension field action as given in 14.4.2.2(b).

2 Bearing stiffener is designed for compressive force due to bearing as given in 14.4.2.2(a).

3 End post is designed for horizontal shear $R_{\mathrm{tf}}$ and moment $M_{\mathrm{tf}}$ as given in 14.5.3.

14.5.4 Panels with Openings

Panels with opening of dimension greater than 10 percent of the minimum panel dimension should be designed without using tension field action as given in 14.4.2.2(b). The adjacent panels should be designed as an end panel as given in 14.5.1 or 14.5.2, as appropriate.

14.6Design of Beams and Plate Girders with Solid Webs

14.6.1 Minimum Web Thickness

The thickness of the web in a section shall satisfy the following requirements:

14.6.1.1 Serviceability requirement

a) when transverse stiffeners are not provided,

$\frac{d}{t_{\mathrm{w}}}\leq 200\varepsilon_{\mathrm{w}}$ (web connected to flanges along both longitudinal edges)
$\frac{d}{t_{\mathrm{w}}}\leq 90\varepsilon_{\mathrm{w}}$ (web connected to flanges along one longitudinal edge only),

b) when only transverse stiffeners are provided (in webs connected to flanges along both longitudinal edges),

when $3d \geq c \geq d$

\frac {d}{t _ {\mathrm{w}}} \leq 2 0 0 \varepsilon_ {\mathrm{w}}

when $0.74d\geq c < d$

\frac {c}{t _ {\mathrm{w}}} \leq 2 0 0 \varepsilon_ {\mathrm{w}}

when $c < 0.74d$

\frac {d}{t _ {\mathrm{w}}} \leq 2 7 0 \varepsilon_ {\mathrm{w}}

when $c > 3d$ , the web shall be considered as unstiffened,

c) when transverse stiffeners and longitudinal stiffeners at one level only are provided (0.2 d from compression flange) according to 14.7.13(a),

when $2.4d\geq c\geq d$

\frac {d}{t _ {\mathrm{w}}} \leq 2 5 0 \varepsilon_ {\mathrm{w}}

when $0.74d\leq c\leq d$

\frac {c}{t _ {\mathrm{w}}} \leq 2 5 0 \varepsilon_ {\mathrm{w}}

when c < 0.74 d

\frac {d}{t _ {\mathrm{w}}} \leq 3 4 0 \varepsilon_ {\mathrm{w}}

d) when a second longitudinal stiffener (located at neutral axis is provided)

\frac {d}{t _ {\mathrm{w}}} \leq 4 0 0 \varepsilon_ {\mathrm{w}}

where

$d =$ depth of the web,

$t_\mathrm{w} =$ thickness of the web,

c = spacing of transverse stiffener (see Fig. 12 and Fig. 13),

$\varepsilon_{\mathrm{w}} =$ yield stress ratio of web $= \sqrt{\frac{250}{f_{\mathrm{yw}}}}$ and

$f_{\mathrm{yw}} =$ yield stress of the web.

14.6.1.2 Compression flange buckling requirement

In order to avoid buckling of the compression flange into the web, the web thickness shall satisfy the following:

a) When transverse stiffeners are not provided,

\frac {d}{t _ {\mathrm{w}}} \leq 3 4 5 \varepsilon_ {\mathrm{f}} ^ {2}

b) When transverse stiffeners are provided, and

i) when $c\geq 1.5d$

\frac {d}{t _ {\mathrm{w}}} \leq 3 4 5 \varepsilon_ {\mathrm{f}} ^ {2}

ii) when $c < 1.5d$

\frac {d}{t _ {\mathrm{w}}} \leq 3 4 5 \varepsilon_ {\mathrm{f}}

where

$d =$ depth of the web,

$t_\mathrm{w} =$ thickness of the web,

c = spacing of transverse stiffener (see Fig. 12 and Fig. 13),

$\varepsilon_{\mathrm{f}} =$ yield stress ratio of flange $= \sqrt{\frac{250}{f_{\mathrm{yf}}}}$ , and

$f_{\mathrm{yf}} =$ yield stress of compression flange.

14.6.2 Sectional Properties

14.6.2.1 The effective sectional area of compression flanges shall be the gross area with deductions for excessive width of plates as specified for compression members [see Section 6(g)] and for open holes occurring in a plane perpendicular to the direction of stress at the section being considered (see 14.2.1.4).

The effective sectional area of tension flanges shall be the gross sectional area with deductions for holes as specified in 14.2.1.4.

The effective sectional area for parts in shear shall be taken as specified in 14.4.1.1.

14.6.3 Flanges

14.6.3.1 In riveted or bolted construction, flange angles shall form as large a part of the area of the flange as practicable (preferably not less than one-third) and the number of flange plates shall be kept to a minimum.

In exposed situations, where flange angles are used, at least one plate of the top flange shall extend over the full length of the girder, unless the top edge of the web is machined flush with the flange angles. Where two or more flange plates are used, tacking rivets shall be provided, if necessary to comply with the requirements of Section 6(k).

Each flange plate shall extend beyond its theoretical cut-off point, and the extension shall contain sufficient rivets, bolts or welds to develop in the plate, the load calculated for the bending moment on the girder section

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

(taken to include the curtailed plate) at the theoretical cut-off point.

The outstand of flange plates, that is the projection beyond the outer line of connections to flange angles, channel or joist flanges or in the case of welded constructions their projection beyond the face of the web or tongue plate, shall not exceed the values given in 9.7.2 (see Table 2).

In the case of box girders, the thickness of any plate, or the aggregate thickness of two or more plates, when these plates are tacked together to form the flange, shall satisfy the requirements given in 9.7.2 (see Table 2).

14.6.3.2 Flange splices

Flange splices should preferably, not be located at points of maximum stress. Where splice plates are used, their area shall be not less than 5 percent in excess of the area of the flange element spliced; their centre of gravity shall coincide, as nearly as possible, with that of the element spliced. There shall be enough bolts, rivets or welds on each side of the splice to develop the load in the element spliced plus 5 percent but in no case should the strength developed be less than 50 percent of the effective strength of the material spliced. In welded construction, flange plates shall be joined by complete penetration butt welds, wherever possible. These butt welds shall develop the full strength of the plates.

14.6.3.3 Connection of flanges to web

The flanges of plate girders shall be connected to the web by sufficient rivets, bolts or welds to transmit the maximum horizontal shear force resulting from the bending moment gradient in the girder, combined with any vertical loads which are directly applied to the flange. If the web is designed using tension field method as given in 14.4.2.2 b), the weld should be able to transfer the tension field stress, $f_{\mathrm{yw}}$ acting on the web.

14.6.3.4 Bolted/Riveted construction

For girders in exposed situations and which do not have flange plates for their entire length, the top edge of the web plate shall be flush with or above the angles, and the bottom edge of the web plate shall be flush with or set back from the angles.

14.6.3.5 Welded construction

The gap between the web plates and flange plates shall be kept to a minimum and for fillet welds shall not exceed 1 mm at any point before welding.

14.6.4 Webs

14.6.4.1 Effective sectional area of web of plate girder

The effective cross-sectional area shall be taken as the full depth of the web plate multiplied by the thickness.

NOTE — Where webs are varied in thickness in the depth of the section by the use of tongue plates or the like, or where the proportion of the web included in the flange area is 25 percent or more of the overall depth, the above approximation is not permissible and the maximum shear stress shall be computed on theory.

14.6.4.2 Splices in webs

Splices and cutouts for service ducts in the webs should preferably not be located at points of maximum shear force and heavy concentrated loads.

Splices in the webs of the plate girders and rolled sections shall be designed to resist the shears and moments at the spliced section (see Annex E).

In riveted or bolted construction, splice plates shall be provided on each side of the web. In welded construction, web splices shall preferably be made with complete penetration butt welds.

14.6.4.3 Where additional plates are required to augment the strength of the web, they shall be placed on each side of the web and shall be equal in thickness. The proportion of shear force assumed to be resisted by these plates shall be limited by the amount of horizontal shear which they can transmit to the flanges through their fastenings, and such reinforcing plates and their fastenings shall be carried up to the points at which the flange without the additional plates is adequate.

14.7Stiffener Design

14.7.1 General

14.7.1.1 When the web of a member acting alone (that is, without stiffeners) proves inadequate, stiffeners for meeting the following requirements should be provided:

a) Intermediate transverse web stiffener — To improve the buckling strength of a slender web due to shear (see 14.7.2).

b) Load carrying stiffener — To prevent local buckling of the web due to concentrated loading (see 14.7.3 and 14.7.5).

c) Bearing stiffener — To prevent local crushing of the web due to concentrated loading (see 14.7.4 and 14.7.6).

d) Torsion stiffener — To provide torsional restraint to beams and girders at supports (see 14.7.9).

e) Diagonal stiffener — To provide local reinforcement to a web under shear and bearing (see 14.7.7).

f) Tension stiffener — To transmit tensile forces applied to a web through a flange (see 14.7.8).

The same stiffeners may perform more than one function and their design should comply with the requirements of all the functions for which designed.

14.7.1.2 Outstand of web stiffeners

Unless the outer edge is continuously stiffened, the outstand from the face of the web should not exceed $20t_{q}\varepsilon$ .

When the outstand of web stiffener is between $14t_{q}\varepsilon$ and $20t_{q}\varepsilon$ , then the stiffener design should be on the basis of a core section with an outstand of only $14t_{q}\varepsilon$ , where $t_{q}$ is the thickness of the stiffener.

14.7.1.3 Stiff bearing length

The stiff bearing length of any element, $b_{1}$ , is that length which cannot deform appreciably in bending. To determine $b_{1}$ , the dispersion of load through a steel bearing element should be taken as $45^{\circ}$ through solid material, such as bearing plates, flange plates, etc (see Fig.15).

14.7.1.4 Eccentricity

Where a load or reaction is applied eccentric to the centerline of the web or where the centroid of the stiffener does not lie on the centerline of the web, the resulting eccentricity of loading should be accounted for in the design of the stiffener.

14.7.1.5 Buckling resistance of stiffeners

The buckling resistance $F_{\mathrm{qd}}$ should be based on the design compressive stress $f_{\mathrm{cd}}$ (see 13.1.2.1) of a strut (curve c), the radius of gyration being taken about the axis parallel to the web. The effective section is the full area or core area of the stiffener (see 14.7.1.2) together with an effective length of web on each side of the centerline of the stiffeners, limited to 20 times the web thickness. The design strength used should be the minimum value obtained for buckling about the web or the stiffener.

The effective length for intermediate transverse stiffeners used in calculating the buckling resistance,

$F_{\mathrm{qd}}$ , should be taken as 0.7 times the length, $L$ of the stiffener.

The effective length for load carrying web stiffeners used in calculating the buckling resistance, $F_{xd}$ , assumes that the flange through which the load or reaction is applied is effectively restrained against lateral movement relative to the other flange, the effective length should be taken as:

a) $KL = 0.7L$ , when flange is restrained against rotation in the plane of the stiffener (by other structural elements), and

b) $KL = L$ , when flange is not so restrained

where

$L =$ length of the stiffener.

If the load or reaction is applied to the flange by a compression member, then unless effective lateral restraint is provided at that point, the stiffener should be designed as part of the compression member applying the load, and the connection between the column and beam flange shall be checked for the effects of the strut action.

14.7.2 Design of Intermediate Transverse Web Stiffeners

14.7.2.1 General

Intermediate transverse stiffeners may be provided on one or both sides of the web.

14.7.2.2 Spacing

Spacing of intermediate stiffeners, where provided, shall comply with 14.6.1 depending on the thickness of the web.

14.7.2.3 Outstand of stiffeners

The outstand of the stiffeners should comply with 14.7.1.2.

FIG. 15 STIFF BEARING LENGTH, $b_{1}$

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

14.7.2.4 Minimum stiffeners

Transverse web stiffeners not subject to external loads or moments should have a second moment of area, $I_{s}$ about the centreline of the web, if stiffeners are on both sides of the web and about the face of the web, if single stiffener on only one side of the web is used such that:

\text {if} \frac {c}{d} \geq \sqrt {2}, I _ {s} \geq 0. 7 5 d t _ {\mathrm{w}} ^ {3}, \text {and}

\text {if} \left. c / d < \sqrt {2}, I _ {\mathrm{s}} \geq \frac {1 . 5 d ^ {3} t _ {\mathrm{w}} ^ {3}}{c ^ {2}} \right.

where

$d =$ depth of the web;

$t_{w}$ = minimum required web thickness for spacing using tension field action, as given in 14.4.2.1; and

$c =$ actual stiffener spacing.

14.7.2.5 Buckling check on intermediate transverse web stiffeners

Stiffeners not subjected to external loads or moments should be checked for a stiffener force:

F _ {\mathrm{q}} = V - V _ {\mathrm{cr}} / \gamma_ {\mathrm{m0}} \leq F _ {\mathrm{qd}}

where

$F_{qd} = \text{design resistance of the intermediate stiffeners;}$

$V =$ factored shear force adjacent to the stiffener; and

$V_{cr}$ = shear buckling resistance of the web panel designed without using tension field action as given in 14.4.2.2 a).

Stiffeners subject to external loads and moments should meet the conditions for load carrying web stiffeners in 14.7.3. In addition they should satisfy the following interaction expression:

\frac {F _ {\mathrm{q}} - F _ {\mathrm{x}}}{F _ {\mathrm{qd}}} + \frac {F _ {\mathrm{x}}}{F _ {\mathrm{xd}}} + \frac {M _ {\mathrm{q}}}{M _ {\mathrm{yq}}} \leq 1

where

$F_{\mathrm{q}} =$ stiffener force given above;

$F_{qd} =$ design resistance of an intermediate web stiffener corresponding to buckling about an axis parallel to the web (see 14.7.1.5);

F _ {\mathrm{x}} = \text {external load or reaction at the stiffener;}

$F_{xd} =$ design resistance of a load carrying stiffener corresponding to buckling about axis parallel to the web (see 14.7.1.5);

$M_{q} =$ moment on the stiffener due to eccentrically applied load and transverse load, if any; and

$M_{yq} =$ yield moment capacity of the stiffener based on its elastic modulus about its centroidal axis parallel to the web.

If $F_{\mathrm{q}} < F_{\mathrm{x}}$ , then $(F_{\mathrm{q}} - F_{\mathrm{x}})$ should be taken as zero;

14.7.2.6 Connection of intermediate stiffeners to web

Intermediate transverse stiffeners not subject to external loading should be connected to the web so as to withstand a shear between each component of the stiffener and the web (in kN/mm) of not less than:

t _ {\mathrm{w}} ^ {2} / \left(5 b _ {\mathrm{s}}\right)

where

$t_{w} = \text{web thickness, in mm; and}$

$b_{\mathrm{s}} =$ outstand width of the stiffener, in mm.

For stiffeners subject to external loading, the shear between the web and the stiffener due to such loading has to be added to the above value.

Stiffeners not subject to external loads or moments may terminate clear of the tension flange and in such a situation the distance cut short from the line of the weld should not be more than $4t_{w}$ .

14.7.3 Load Carrying Stiffeners

14.7.3.1 Web check

Load carrying web stiffeners should be provided where compressive forces applied through a flange by loads or reactions exceed the buckling strength, $F_{cdw}$ , of the unstiffened web, calculated using the following:

The effective length of the web for evaluating the slenderness ratio is calculated as in 14.7.1.5. The area of cross-section is taken as $(b_{1} + n_{1})t_{\mathrm{w}}$ .

where

$b_{1}$ = width of stiff bearing on the flange (see 14.7.1.3), and

$n_{1}$ = dispersion of the load through the web at $45^{\circ}$ , to the level of half the depth of the cross-section.

The buckling strength of this web about axis parallel to the web is calculated as given in 13.1.2.1, using curve 'c'.

14.7.4 Bearing Stiffeners

Bearing stiffeners should be provided for webs where forces applied through a flange by loads or reactions exceeding the local capacity of the web at its connection to the flange, $F_{w}$ , given by:

F _ {\mathrm{w}} = \left(b _ {1} + n _ {2}\right) t _ {\mathrm{w}} f _ {\mathrm{yw}} / \gamma_ {\mathrm{m0}}

where

b _ {1} = \text {stiff bearing length (see 14.7.1.3),}

$n_{2}$ = length obtained by dispersion through the flange to the web junction at a slope of 1:2.5 to the plane of the flange,

$t_{w}$ = thickness of the web, and

$f_{\mathrm{yw}} =$ yield stress of the web.

14.7.5 Design of Load Carrying Stiffeners

14.7.5.1 Buckling check

The external load or reaction, $F_{\mathrm{x}}$ on a stiffener should not exceed the buckling resistance, $F_{\mathrm{xd}}$ of the stiffener as given in 14.7.1.5.

Where the stiffener also acts as an intermediate stiffener it should be checked for the effect of combined loads in accordance with 14.7.2.5.

14.7.5.2 Bearing check

Load carrying web stiffeners should also be of sufficient size that the bearing strength of the stiffener, $F_{\mathrm{psd}}$ , given below is not less than the load transferred, $F_{\mathrm{x}}$

F _ {\mathrm{psd}} = A _ {\mathrm{q}} f _ {\mathrm{yq}} / (0. 8 \gamma_ {\mathrm{m0}}) \geq F _ {\mathrm{x}}

where

$F_{\mathrm{x}} =$ external load or reaction,

$A_{q}$ = area of the stiffener in contact with the flange, and

$f_{\mathrm{yq}} =$ yield stress of the stiffener.

14.7.6 Design of Bearing Stiffeners

Bearing stiffeners should be designed for the applied load or reaction less the local capacity of the web as given in 14.7.4. Where the web and the stiffener material are of different strengths the lesser value should be assumed to calculate the capacity of the web and the stiffener. Bearing stiffeners should project nearly as much as the overhang of the flange through which load is transferred.

14.7.7 Design of Diagonal Stiffeners

Diagonal stiffeners should be designed to carry the portion of the applied shear and bearing that exceeds the capacity of the web.

Where the web and the stiffener are of different strengths, the value for design should be taken as given in 14.7.6.

14.7.8 Design of Tension Stiffeners

Tension stiffeners should be designed to carry the portion of the applied load or reaction less the capacity of the web as given in 14.7.4 for bearing stiffeners.

Where the web and the stiffener are of different strengths, the value for design should be taken as given in 14.7.6.

14.7.9 Torsional Stiffeners

Where bearing stiffeners are required to provide torsional restraint at the supports of the beam, they should meet the following criteria:

a) Conditions of 14.7.4, and

b) Second moment of area of the stiffener section about the centerline of the web, $I_{\mathrm{s}}$ should be such that:

I _ {\mathrm{s}} \geq 0. 3 4 \alpha_ {\mathrm{s}} D ^ {3} T _ {\mathrm{cf}}

where

\alpha_ {\mathrm{s}} = 0. 0 0 6 \text {for} L _ {\mathrm{LT}} / r _ {\mathrm{y}} \leq 5 0;

= 0. 3 / (L _ {\mathrm{LT}} / r _ {\mathrm{y}}) \text {for} 5 0 < L _ {\mathrm{LT}} / r _ {\mathrm{y}} \leq 1 0 0;

= 3 0 / (L _ {\mathrm{LT}} / r _ {\mathrm{y}}) ^ {2} \text {for} L _ {\mathrm{LT}} / r _ {\mathrm{y}} > 1 0 0;

$D =$ Overall depth of beam at support,

$T_{\mathrm{cf}} =$ Maximum thickness of compression flange in the span under consideration,

$KL =$ Laterally unsupported effective length of the compression flange of the beam, and

$r_{y}$ = Radius of gyration of the beam about the minor axis.

14.7.10 Connection to Web of Load Carrying and Bearing Stiffeners

Stiffeners, which resist loads or reactions applied through a flange, should be connected to the web by sufficient welds or fasteners to transmit a design force equal to the lesser of,

a) tension capacity of the stiffener; and

b) sum of the forces applied at the two ends of the stiffener when they act in the same direction or the larger of the forces when they act in opposite directions.

Stiffeners, which do not extend right across the web, should be of such length that the shear stress in the web due to the design force transmitted by the stiffener does not exceed the shear strength of the web. In addition, the capacity of the web beyond the end of the stiffener should be sufficient to resist the applied force.

14.7.11 Connection to Flanges

14.7.11.1 In tension

Stiffeners required to resist tension should be connected to the flange transmitting the load by continuous welds or non-slip fasteners.

14.7.11.2 In compression

Stiffeners required to resist compression should either be fitted against the loaded flange or connected by continuous welds or non-slip fasteners.

The stiffener should be fitted against or connected to both flanges when,

PART 6 STRUCTURAL DESIGN — SECTION 6 STEEL

a) a load is applied directly over a support; or

b) it forms the end stiffener of a stiffened web; or

c) it acts as a torsion stiffener.

14.7.12 Hollow Sections

Where concentrated loads are applied to hollow sections consideration should be given to local stresses and deformations and the section reinforced as necessary.

14.7.13 Horizontal Stiffeners

Where horizontal stiffeners are used in addition to vertical stiffeners, they shall be as follows:

a) One horizontal stiffener shall be placed on the web at a distance from the compression flange equal to 1/5 of the distance from the compression flange angle, plate or tongue plate to the neutral axis when the thickness of the web is less than the limits specified in 14.6.1. The stiffener shall be designed so that $I_{\mathrm{s}}$ is not less than $4ct_{\mathrm{w}}^{3}$ where $I_{\mathrm{s}}$ and $t_{\mathrm{w}}$ are as defined in 14.7.2.4 and $c$ is the actual distance between the vertical stiffeners;

b) A second horizontal stiffener (single or double) shall be placed at the neutral axis of the girder when the thickness of the web is less than the limit specified in 14.6.1. This stiffener shall be designed so that $I_{\mathrm{s}}$ is not less than $d_2 t_{\mathrm{w}}^3$ where $I_{\mathrm{s}}$ and $t_{\mathrm{w}}$ are as defined in 14.7.2.4 and $d_2$ is twice the clear distance from the compression flange angles, plates or tongue plates to the neutral axis;

c) Horizontal web stiffeners shall extend between vertical stiffeners, but need not be continuous over them; and

d) Horizontal stiffeners may be in pairs arranged on each side of the web, or single located on one side of the web.

14.8 Box Girders

The design and detailing of box girders shall be such as to give full advantage of its higher load carrying capacity. Box girder shall be designed in accordance with specialist literature. The diaphragms and horizontal stiffeners should conform to 14.7.12 and 14.7.13.

14.8.1 All diaphragms shall be connected so as to transfer the resultant shears to the web and flanges.

14.8.2 Where the concentrated or moving load does not act directly on top of the web, the local effect shall be considered in the design of flanges and the diaphragms.