Restrained Beams

1. In a restrained beam, the top flange of the beam is restrained by a lateral restraint2. Beam to be checked for –

a. Adequacy of lateral restrainti. The restraining system (Ex: floor system) shall resist not less than 2.5%

of maximum force in compression flange (Force in comp. flange = Moment/depth)

b. Section classification i. Elements of a section can be classified as Plastic (Class-1), Compact,

Semi compact and Slender (Class-4) based on moment/rotation characteristics and load conditions

ii. Moment capacity of the section depends on section classificationiii. Once section classification is determined, moment capacity is

calculated accordingly, elements are deemed not to buckle. So no separate buckling check required for elements

c. Sheari. Shear capacity for thick webs, shear buckling resistance for thin webs

(shear buckling happens only in plate girders)ii. Shear capacity = 0.6*Py * Av

d. Combined Bending and sheari. For low shear (Shear force < 60% of Shear capacity)

Mc = Py * S for Plastic and compact, Py * Z for Semi compact and Py * Zeff for slender sections

ii. For high shear (Shear force > 60% of Shear capacity)

Mc = Py * (S-ρSv) (ρ is ratio of shear capacity, Sv Plastic modulus of shear area)

iii. For all cases, Mc <=1.2*py Z

e. Web bearing and bucklingWhen load is applied from the top flange directly, web to be

checked for bearing and bucklingf. Deflection

i. For beams, L/180 – L/200ii. For columns L/300

Unrestrained Beams

1. In an unrestrained beam, the top flange of the beam will buckle laterally if not restrained, causing lateral torsional buckling

2. Buckling resistance is influenced by – i. Span

ii. Type of end connectionsiii. Load location and whether load is free to move along with beamiv. Lateral bending stiffnessv. Torsional stiffness of the beam

3. Equivalent slenderness of the beam λLT will account for all above factors4. Unrestrained beams shall be designed for moment capacity and buckling resistance5. Moment capacity calculation same as earlier6. Buckling resistance

a. Mb = Mx/Mltb. Bending strength Mx = λLT * pyc. Equivalent length of member is based on type of connection at endsd. Equivalent moment factor Mlt - depends on unequal moment distribution

across member.