Steel Beam Design as per BS 5950

An overview of the procedures that need to be followed in steel beam design is discussed in this article. There are basic steps to be followed to complete the design. These steps can be categorized into six main subjects according to the BS 5950.

The following steps in the following order could be followed to do the design correctly. 

1. Section Classification
2. Shear Capacity
3. Bending Capacity
4. Lateral Torsional Buckling
5. Deflection
6. Web Bearing
7. Web Buckling

Classification of Section

Classification is done based on the aspect ratios of the section.

Based on the b/t and d/t flange and web are classified under the categories Plastic, Compact, Semi-Compact, and Slender sections. Click here for more on the Classification of sections.

Further, the first step of the steel beam design is the classification of the section. No design shall be carried out without classifying the beam.

Shear Capacity

P_v = 0.6P_yA_v

P_v > F_v

Where

P_v – Design shear strength

F_v – Design Shear Force

Av is the shear area and it shall be calculated as stipulated in the BS 5950. For rolled I and H sections and channel sections, load parallel to the web

A_v = tD

Bending Capacity

The bending capacity equation in steel beam design is selected based on the shear force in the section. 

There are different sets of equations for Low Shear ( F_v ≤ 0.6P_v ) and High Shear ( F_v ≥ 0.6P_v ).

Further, for avoiding irreversible deformation under service loads, the value of Mc should be limited to 1.5P_yZ generally and to 1.2P_yZ in the case of the simply supported beam or cantilever.

Low Shear ( F_v ≤ 0.6P_v )

Section Classification	Moment Capacity
Class 1 – Plastic Class 2 – Compact	Mc = PyS
Class 3 – Semi-Compact	Mc = Py Z or Mc = PySeff
Class 4 – Slender	Mc = PyZeff

Where,

S – Plastic Section Modulus

S_eff – Effective Plastic Modulus

Z – Section Modulus – Elastic

Z_eff – Effective Elastic Section Modulus

High Shear ( F_v ≥ 0.6P_v )

Section Classification	Moment Capacity
Class 1 – Plastic Class 2 – Compact	Mc = Py(S – ρSv)
Class 3 – Semi-Compact	Mc = Py(Z – ρSv/1.5) or Mc = Py( Seff – ρSv)
Class 4 – Slender	Mc = Py( Zeff – ρSv/1.5)

Based on the classification of the section and after check the low shear and high shear conditions, bending capacity can be evaluated.

For more information on other checks to be done can be referred by clicking the relevant item from the above list of checks.

Lateral Torsional Buckling

Beam shall be checked for the lateral torsional buckling base on its span and as per the arrangement of the internal supports. The article lateral torsional buckling could be referred for theoretical and worked example. 

Steel beam design shall include a lateral-torsional buckling check. It shall not be avoided due to any reason.

Deflection

Beam shall be checked for the vertical deflection considering the imposed loads applied on the beam. Table 8 of BS 5950: 2000 indicates the limiting values to be considered for the design.

Deflection due to the design loads could be calculated manually or it could be obtained from the analysis. For example, the maximum deflection of a simply supported beam having loaded with uniformly distributed load can be obtained from the following equation.

δ = 5W_eL⁴ / (384EI)

Similarly, from literature or analysis, defection due to the loading can be calculated.

A deflection check shall be done in the steel beam design to make sure there are no excessive deflection. 

The Wikipedia article deflection (engineering) states the methods of calculation deflections.

Web Bearing

The bearing capacity of the web is checked to make sure it can carry the vertical loads applied to it. When required by the design, stiffeners are provided to improve the stiffness of the web.

Web Bearing Capacity, P_bw

P_bw = (b₁ + nk) tP_yw

Where

b₁ – bearing length to be calculated based on the location

n = (2 + 0.6b_e/k) but ≤ 5 at the end of member and all other cases n = 5

k = T+ r – for rolled I and H sections and

k = T – for welded sections

r = root radius from section table

t = web thickness

P_yw = design strength of the web

For further clarification, a worked example could be referred to.

Web Buckling

Rotation of the flange relative to the web and the lateral movement between the flange are due to the buckling of the web. Depending on the distance to the load center, there are different equations to be used to calculate the capacity of the web.

Web Load Capacity (Px) when the distance to load or reaction to the nearer end similar or grater than 0.7d; ( a_e ≥ 0.7d )

P_x = 25εt P_bw /√[ ( b₁ + nk ) d ]

When a_e < 0.7d

P_x = [ (a_e +0.7d)/1.4d] {25εt P_bw /√[ ( b₁ + nk ) d ] }

In the case, the flange is not restrained against rotation

P_xr = 0.7d P_bw / L_E

As discussed in this article, all the checks shall be done when steel beam design. Worked examples in this web site could be referred for getting aware of the applicability of these equations.