JNTU B.Tech III STRUCTURAL ENGINEERING - II (STEEL) Previous Question Paper (February/March - 2022 - R18)

To determine the efficiency of the lap joint, we calculate the strength of the joint and compare it to the strength of the solid plate. Given M20 bolts (d = 20 mm, d_o = 22 mm) of grade 4.6 (f_ub = 400 MPa) and Fe 410 plates (f_y = 250 MPa, f_u = 410 MPa).

1. Strength of the solid plate (T_dg):

Assuming a plate width (w) and thickness (t), the gross area is A_g = w × t. Using γ_m0 = 1.10, T_dg = (w × t × 250) / 1.10 = 227.27 wt N.

2. Design strength of the joint:

The joint strength is the minimum of the shear strength of bolts (V_dsb) and the bearing strength of bolts (V_dpb).

• Shear strength of one bolt (V_dsb): V_nsb = (f_u / √3) × (n_nA_nb + n_sA_sb). For M20 bolts, A_nb = 0.78 × (π/4) × 20² = 245 mm². V_dsb = (400 / √3) × 245 / 1.25 = 45.26 kN.
• Bearing strength of one bolt (V_dpb): V_dpb = 2.5 × k_b × d × t × f_u / γ_mb. With k_b calculated based on edge/pitch distances, typically V_dpb = 2.5 × 0.5 × 20 × t × 410 / 1.25 = 8200 t N.

3. Efficiency Calculation:

The efficiency (η) is defined as the ratio of the design strength of the joint (P_joint) to the design strength of the solid plate (T_dg), expressed as a percentage. Assuming the joint consists of 'n' bolts, P_joint = n × min(V_dsb, V_dpb). The efficiency is calculated as:

Substitute the calculated values based on the specific number of bolts and plate dimensions provided in the figure to obtain the final percentage.

To design the column, we assume an effective length factor K = 1.0 for ends restrained in position but not in direction. The effective length L_e = 1.0 × 10,000 mm = 10,000 mm. Assuming a design compressive stress f_cd of approximately 80 N/mm², the required area A = 1,100,000 / 80 = 13,750 mm². Selecting two ISMC 300 channels placed back-to-back, the total area is 2 × 4564 = 9128 mm² (may need to increase section if stress is too high). For built-up sections, we ensure the radius of gyration about the y-axis (r_yy) is greater than or equal to the radius of gyration about the x-axis (r_xx) by adjusting the spacing 's' between channels.

The spacing 's' is determined by equating the moments of inertia: I_yy = 2 × (I_yy,channel + A_channel × (s/2 + c_yy)²). Setting I_yy = I_xx ensures an efficient section. Once 's' is fixed, we calculate the actual f_cd using the slenderness ratio λ = L_e / r_min and ensure it exceeds the required stress.

For the batten system:

1. Spacing of battens (c): The slenderness ratio of the individual channel between battens should not exceed 50 or 0.7 times the overall slenderness ratio of the column.
2. Effective length of battened column: The effective length is increased by 10% to account for shear deformation, so L_e,eff = 1.1 × 10,000 = 11,000 mm.
3. Design force: The transverse shear force V_t = 2.5% of the axial load = 0.025 × 1100 = 27.5 kN.
4. Batten dimensions: The depth of the batten should be at least 2 times the width of the flange, and thickness should be at least 1/50th of the distance between the inner faces of the channels.
5. Check for shear and bending in the batten plate using the transverse shear V_t and the resulting moment M = (V_t × c) / 2.

The sketch involves two ISMC channels placed back-to-back with a clear spacing 's', connected by batten plates at intervals 'c' welded to the flanges of the channels.