4.5Plastic Analysis

IS 800:2007, General Construction in Steel — Code of Practice

Last Updated 29 Oct 2026

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4.5.1 Application

The effects of design action throughout or on part of a structure may be determined by a plastic analysis, provided that the requirements of 4.5.2 are met. The distribution of design action effects shall satisfy equilibrium and the boundary conditions.

4.5.2 Requirements

When a plastic method of analysis is used, all of the following conditions shall be satisfied, unless adequate ductility of the structure and plastic rotation capacity of its members and connections are established for the design loading conditions by other means of evaluation:

a) The yield stress of the grade of the steel used shall not exceed 450 MPa.
b) The stress-strain characteristics of the steel shall not be significantly different from those obtained for steels complying with IS 2062 or equivalent and shall be such as to ensure complete plastic moment redistribution. The stress-strain diagram shall have a plateau at the yield stress, extending for at least six times the yield strain. The ratio of the tensile strength to the yield stress specified for the grade of the steel shall not be less than 1.2. The elongation on a gauge length complying with IS 2062 shall not be than 15 percent, and the steel shall exhibit strain-hardening capability. Steels conforming to IS 2062 shall be deemed to satisfy the above requirements.
c) The members used shall be hot-rolled or fabricated using hot-rolled plates and sections.
d) The cross-section of members not containing plastic hinges should be at least that of compact section (see 3.7.2), unless the members meet the strength requirements from elastic analysis.
e) Where plastic hinges occur in a member, the proportions of its cross-section should not exceed the limiting values for plastic section given in 3.7.2.
f) The cross-section should be symmetrical about its axis perpendicular to the axis of the plastic hinge rotation.
g) The members shall not be subject to impact loading, requiring fracture assessment or

fluctuating loading, requiring a fatigu assessment (see Section 13).

4.5.2.1 Restraints

If practicable, torsional restraint (against lateral buckling) should be provided at all plastic hinge locations. Where not feasible, the restraint should be provided within a distance of $D / 2$ of the plastic hinge location, where $D$ is the total depth of section.

The torsional restraint requirement at a section as above, need not be met at the last plastic hinge to form, provided it can be clearly identified.

Within a member containing a plastic hinge, the maximum distance $L_{\mathrm{m}}$ from the restraint at the plastic hinge to an adjacent restraint should be calculated by any rational method or the conservative method given below, so as to prevent lateral buckling.

Conservatively $L_{\mathrm{m}}$ (in mm) may be taken as

$L_{\mathrm{m}} \leq \frac{38 r_{\mathrm{y}}}{\left[\frac{f_{\mathrm{c}}}{130}+\left(\frac{f_{\mathrm{y}}}{250}\right)^{2}\left(\frac{x_{\mathrm{t}}}{40}\right)^{2}\right]^{1/2}}$

where

$f_{\mathrm{c}}=$ actual compressive stress on the cross section due to axial load, in $\mathrm{N} / \mathrm{mm}^{2}$ ;
$f_{\mathrm{y}}=$ yield stress, in $\mathrm{N} / \mathrm{mm}^{2}$
$\begin{aligned} r_{y} & =\text { radius of gyration about the minor axis, in } \\ & \mathrm{mm} ;\end{aligned}$
$x_{\mathrm{t}}=$ torsional index, $x_{\mathrm{t}}=1.132\left(A I_{\mathrm{w}} / I_{\mathrm{y}} I_{\mathrm{t}}\right)^{0.5}$
A= area of cross-section; and

= warping constant, second moment of the cross section above the minor axes and St. Venant's torsion constant, respectively.

Where the member has unequal flanges, $r_{y}$ should be taken as the lesser of the values of the compression flange only or the whole section.

Where the cross-section of the member varies within the length $L_{m}$ , the maximum value of $r_{y}$ and the minimum value of $x_{\mathrm{i}}$ should be used.

The spacing of restraints to member lengths not containing a plastic hinge should satisfy the recommendations of section on lateral buckling strength of beams (see 8.2.2). Where the restraints are placed at the limiting distance $L_{\mathrm{m}}$ , no further checks are required.

4.5.2.2 Stiffeners at plastic hinge locations

Web stiffeners should be provided where a concentrated load, which exceeds 10 percent of the shear capacity

of the member, is applied within $D / 2$ of a plastic hinge location (see 8.2.1.2). The stiffener should be provided within a distance of half the depth of the member on either side of the hinge location and be designed to carry the applied load in accordance with 8.7.4. If the stiffeners are flat plates, the outstand width to the thickness ratio, $b / t$ , should not exceed the values given in the plastic section (see 3.7, Table 2). Where other

sections are used the ratio $\left(\frac{I_{\mathrm{so}}}{I_{\mathrm{t}}}\right)^{1 / 2}$ should not exceed

the values given for plastic section (for simple outstand as in 3.7);

where

$\begin{aligned} I_{\mathrm{so}} & =\text { second moment of area of the stiffener about } \\ & \text { the face of the element perpendicular to the } \\ & \text { web; and }\end{aligned}$

$\begin{aligned} I_{\mathrm{t}} & =\text { St. Venant's torsion constant of the stiffener }\end{aligned}$

4.5.2.3

The frame shall be adequately supported against sway and out-of-plane buckling, by bracings, moment resisting frame or an independent system such as shear wall.

4.5.2.4 Fabrication restriction

Within a length equal to the member depth, on either side of a plastic hinge location, the following restrictions should be applied to the tension flange and noted in the design drawings. Holes if required, should be drilled or else punched 2 mm undersize and reamed. All sheared or hand flame cut edges should be finished smooth by grinding, chipping or planning.

4.5.3 Assumptions in Analysis

The design action effects shall be determined using a rigid-plastic analysis.

It shall be permissible to assume full strength or partial strength connections, provided the capacities of these are used in the analysis, and provided that

a) in a full strength connection, the moment capacity of the connection shall be not less than that of the member being connected;
b) in a partial strength connection, the moment capacity of the connection may be less than that of the member being connected; and
c) in both cases the behaviour of the connection shall be such as to allow all plastic hinges necessary for the collapse mechanism to develop, and shall be such that the required plastic hinge rotation does not exceed the rotation capacity at any of the plastic hinges in the collapse mechanism.

In the case of building structures, it is not normally necessary to consider the effect of alternating plasticity

4.5.4 Second-Order Elastic Analysis

Any second-order effects of the loads acting on the structure in its deformed configuration may be neglected, provided the following are satisfied:

a) For clad frames, provided the stiffening effects of masonry infill wall panels or diaphragms of profiled wall panel is not taken into account, and where elastic buckling load factor, $\lambda_{\mathrm{cr}}$ (see 4.6) satisfies $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 10$ . If $10>\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 4.6$ the second-order effects may be considered by amplifying the design load effects obtained from plastic analysis by a factor $\delta_{\mathrm{p}}=\left\{0.9 \lambda_{\mathrm{cr}} /\left(\lambda_{\mathrm{cr}}-1\right)\right\}$ . If $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}}<4.6$ , second-order elasto-plastic analysis or second-order elastic analysis (see 4.4.3) is to be carried out.
b) For un-clad frames or for clad frames where the stiffening effects of masonry infill or dia- phrams of profiled wall panel is taken into account, where elastic buckling load factor, $\lambda_{\mathrm{cr}}$ (see 4.6) satisfies $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 20$ If $20>\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 5.75$ the second-order effects may be considered by amplifying the design load effects obtained from plastic analysis by a factor $\delta_{\mathrm{p}}=\left\{0.9 \lambda_{\mathrm{cr}} /\left(\lambda_{\mathrm{cr}}-1\right)\right\}$ . If $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}}<5.75$ , second-order elasto-plastic analysis or second-order elastic analysis (see 4.4.3) shall be carried out.

4.5Plastic Analysis

IS 800:2007, General Construction in Steel — Code of Practice

Last Updated 29 Oct 2026

Hover any section to copy its link or text, ask Copilot about it, or bookmark it.

4.5.1 Application

4.5.2 Requirements

a) The yield stress of the grade of the steel used shall not exceed 450 MPa.
b) The stress-strain characteristics of the steel shall not be significantly different from those obtained for steels complying with IS 2062 or equivalent and shall be such as to ensure complete plastic moment redistribution. The stress-strain diagram shall have a plateau at the yield stress, extending for at least six times the yield strain. The ratio of the tensile strength to the yield stress specified for the grade of the steel shall not be less than 1.2. The elongation on a gauge length complying with IS 2062 shall not be than 15 percent, and the steel shall exhibit strain-hardening capability. Steels conforming to IS 2062 shall be deemed to satisfy the above requirements.
c) The members used shall be hot-rolled or fabricated using hot-rolled plates and sections.
d) The cross-section of members not containing plastic hinges should be at least that of compact section (see 3.7.2), unless the members meet the strength requirements from elastic analysis.
e) Where plastic hinges occur in a member, the proportions of its cross-section should not exceed the limiting values for plastic section given in 3.7.2.
f) The cross-section should be symmetrical about its axis perpendicular to the axis of the plastic hinge rotation.
g) The members shall not be subject to impact loading, requiring fracture assessment or

fluctuating loading, requiring a fatigu assessment (see Section 13).

4.5.2.1 Restraints

The torsional restraint requirement at a section as above, need not be met at the last plastic hinge to form, provided it can be clearly identified.

Conservatively $L_{\mathrm{m}}$ (in mm) may be taken as

$L_{\mathrm{m}} \leq \frac{38 r_{\mathrm{y}}}{\left[\frac{f_{\mathrm{c}}}{130}+\left(\frac{f_{\mathrm{y}}}{250}\right)^{2}\left(\frac{x_{\mathrm{t}}}{40}\right)^{2}\right]^{1/2}}$

where

$f_{\mathrm{c}}=$ actual compressive stress on the cross section due to axial load, in $\mathrm{N} / \mathrm{mm}^{2}$ ;
$f_{\mathrm{y}}=$ yield stress, in $\mathrm{N} / \mathrm{mm}^{2}$
$\begin{aligned} r_{y} & =\text { radius of gyration about the minor axis, in } \\ & \mathrm{mm} ;\end{aligned}$
$x_{\mathrm{t}}=$ torsional index, $x_{\mathrm{t}}=1.132\left(A I_{\mathrm{w}} / I_{\mathrm{y}} I_{\mathrm{t}}\right)^{0.5}$
A= area of cross-section; and

= warping constant, second moment of the cross section above the minor axes and St. Venant's torsion constant, respectively.

Where the member has unequal flanges, $r_{y}$ should be taken as the lesser of the values of the compression flange only or the whole section.

Where the cross-section of the member varies within the length $L_{m}$ , the maximum value of $r_{y}$ and the minimum value of $x_{\mathrm{i}}$ should be used.

4.5.2.2 Stiffeners at plastic hinge locations

Web stiffeners should be provided where a concentrated load, which exceeds 10 percent of the shear capacity

sections are used the ratio $\left(\frac{I_{\mathrm{so}}}{I_{\mathrm{t}}}\right)^{1 / 2}$ should not exceed

the values given for plastic section (for simple outstand as in 3.7);

where

$\begin{aligned} I_{\mathrm{so}} & =\text { second moment of area of the stiffener about } \\ & \text { the face of the element perpendicular to the } \\ & \text { web; and }\end{aligned}$

$\begin{aligned} I_{\mathrm{t}} & =\text { St. Venant's torsion constant of the stiffener }\end{aligned}$

4.5.2.3

The frame shall be adequately supported against sway and out-of-plane buckling, by bracings, moment resisting frame or an independent system such as shear wall.

4.5.2.4 Fabrication restriction

4.5.3 Assumptions in Analysis

The design action effects shall be determined using a rigid-plastic analysis.

It shall be permissible to assume full strength or partial strength connections, provided the capacities of these are used in the analysis, and provided that

a) in a full strength connection, the moment capacity of the connection shall be not less than that of the member being connected;
b) in a partial strength connection, the moment capacity of the connection may be less than that of the member being connected; and
c) in both cases the behaviour of the connection shall be such as to allow all plastic hinges necessary for the collapse mechanism to develop, and shall be such that the required plastic hinge rotation does not exceed the rotation capacity at any of the plastic hinges in the collapse mechanism.

In the case of building structures, it is not normally necessary to consider the effect of alternating plasticity

4.5.4 Second-Order Elastic Analysis

Any second-order effects of the loads acting on the structure in its deformed configuration may be neglected, provided the following are satisfied:

a) For clad frames, provided the stiffening effects of masonry infill wall panels or diaphragms of profiled wall panel is not taken into account, and where elastic buckling load factor, $\lambda_{\mathrm{cr}}$ (see 4.6) satisfies $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 10$ . If $10>\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 4.6$ the second-order effects may be considered by amplifying the design load effects obtained from plastic analysis by a factor $\delta_{\mathrm{p}}=\left\{0.9 \lambda_{\mathrm{cr}} /\left(\lambda_{\mathrm{cr}}-1\right)\right\}$ . If $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}}<4.6$ , second-order elasto-plastic analysis or second-order elastic analysis (see 4.4.3) is to be carried out.
b) For un-clad frames or for clad frames where the stiffening effects of masonry infill or dia- phrams of profiled wall panel is taken into account, where elastic buckling load factor, $\lambda_{\mathrm{cr}}$ (see 4.6) satisfies $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 20$ If $20>\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}} \geq 5.75$ the second-order effects may be considered by amplifying the design load effects obtained from plastic analysis by a factor $\delta_{\mathrm{p}}=\left\{0.9 \lambda_{\mathrm{cr}} /\left(\lambda_{\mathrm{cr}}-1\right)\right\}$ . If $\lambda_{\mathrm{cr}} / \lambda_{\mathrm{p}}<5.75$ , second-order elasto-plastic analysis or second-order elastic analysis (see 4.4.3) shall be carried out.