V. IS 801-Beam with axial and major axis bending

Verification

Section Dimension Checks

Check for flat width ratio:

Hence, OK (ref. cl 5.2.3(a))

Hence, OK (ref. cl 5.2.3(b))

Check for web height to thickness ratio:

Hence, OK (ref. cl 5.2.4(a))

Check for limiting slenderness

Hence, OK (ref. cl 6.3.3)

Calculation of Allowable Compressive Stress

For calculation of axially loaded member, “ Q ” is an important factor. The definition and method of calculation for value of Q is provided in Clause no. 6.6.1.1 (a). Channel section without lips is a combination of stiffened & unstiffened elements.

As per clause no 6.1.1.1 of IS801, the increase of steel strength happens due to cold work of forming.

Total corner area, A_corner = 2(45.2 mm²) = 91.2 mm² = 0.912 cm²

Total area of flanges, A_flange = 2×b×t = 2(0.4)(0.4) = 3.2 cm²

Effective depth, h_e = h = 4 cm

Therefore, effective area, A_e = A = 4.91 cm²

Tensile yield point of corner,

Tensile yield point of flat portions, F_yt = F_y = 350.0 MPa

Average yield point of cold-forming for tension/compression members, F_{ya(compression)} = (C × F_yc) + (1 - C)×F_yc = 381.8 MPa ( = 3,893 kgf/cm²)

Average yield point of cold-forming for flexural members, F_ya(bending) = (C × F_yc) + (1 - C)×F_yc = 398.8 MPa

As per cl. 6.2 of IS 801, compressive stress:

Allowable compression stress, F_a1 , for members braced against twisting (ref. cl 6.6.1.1)

Slenderness ratio KL/r = 158.3

Maximum allowable compressive stress (Fa2) for flexural-torsional buckling (ref. cl 6.6.1.2 of IS 801)

The allowable compressive stress, F_a is the minimum of F_a1 and F_a2 :

Calculation of Allowable Bending Stress

As per clause number 6.1, maximum allowable stress on extreme fiber is:

As the section is channel without lips, the flanges are unstiffened. So, as per clause 6.2 we need to check allowable compressive stress on the unstiffened element.

Also, the yield strength of steel, F_y > 2,230 kgf/cm² ( = 227.5 MPa).

For the major axis bending, the allowable compressive stress, F_bc , is the minimum of F and F_c

Similarly, for major axis bending, the allowable tensile stress, F_bt=0.6 × F_{ya(compression)} = 229.1 MPa

Calculate the allowable bending stress for laterally unbraced beams:

Allowable bending stress for laterally unbraced beams has been calculated as per clause 6.3 (a).

Unsupported length, L = 2 m (the UNL parameter can be used for this).

C_b = 1.0 for a member under compression and bending.

Allowable bending stress in the web:

Per cl. 6.4.2, F_bw is the minimum of F_bw1 and 0.6 × F_ya(bending) = 239.2 MPa

Calculation of Allowable Shear Stress

Per cl. 6.4:

Clear distance between flanges = h = d - 2t = 52 mm

Allowable shear stress, F_v is the minimum of F_v1 or 0.4 × F_y = 140.1 MPa

Allowable combined bending and shear stress:

As , F_vc = F_vc1 = 577.1 MPa

Actual Stresses

Compression

Bending

Bending in Web

• Actual bending stress in the web is calculated by interpolation of bending stress diagram:

Shear

Stress Ratio

Compression

Bending

• for bending compression: f_b / F_bc = 83.76 / 229.1 = 0.366
• for bending tension: f_b / F_bt = 83.76 / 229.1 = 0.366
• for unbraced bending: f_b / F_b = 83.76 / 85.18 = 0.983
• for web bending: f_bw / F_bw = 72.59 / 239.2 = 0.303

Shear

Combined bending and shear (ref. cl 6.4.3 of IS 801):

Interaction ratio for axial and bending

As Q = 1.0, F_a0 can be calculated using cl. 6.6.1.1(b) with L = 0: