Module 6: Steel Tension Members - Examples & Applications

Determine the LRFD design tensile strength ($\phi P_n$) for an A36 steel plate ($F_y = 250 \text{ MPa}, F_u = 400 \text{ MPa}$) with a gross area $A_g = 2,500 \text{ mm}^2$ and an effective net area $A_e = 1,800 \text{ mm}^2$.

LRFD Factors: $\phi_t = 0.90$ for yielding, $\phi_t = 0.75$ for rupture.

A $15 \text{ mm}$ thick steel plate ($A_g = 4,500 \text{ mm}^2$, total width = $300 \text{ mm}$) is under tension. It is connected using $22 \text{ mm}$ bolts in a staggered pattern. For this worked example, the applicable hole/detailing provision has already established the design hole deduction as $d_h = 24 \\text{ mm}$. Do not treat nominal bolt diameter plus $2 \\text{ mm}$ as a universal hole rule. A critical failure path zig-zags across the plate, passing through 3 holes. The staggered path has two diagonal segments, both with a longitudinal pitch ($s$) of $50 \text{ mm}$ and a transverse gage ($g$) of $75 \text{ mm}$.

Calculate the net area ($A_n$) for this specific failure path.

A steel tension member ($F_y = 345 \text{ MPa}, F_u = 450 \text{ MPa}$, $A_g = 4000 \text{ mm}^2$) is spliced. One end is welded (no holes, $U = 0.85$), and the other end is bolted with 4 large bolts ($A_{holes} = 800 \text{ mm}^2, U = 0.90$). Evaluate the design tensile strength of the entire member.

Determine the Shear Lag Factor ($U$) for an L $150 \times 100 \times 10$ angle connected by its long leg to a gusset plate using a single line of four $20 \text{ mm}$ bolts spaced at $75 \text{ mm}$ on center.

Given Parameters:

• Centroid distance from the connected leg ($\bar{x}$): $28 \text{ mm}$
• Number of bolts in line ($n$): $4$
• Bolt spacing ($s$): $75 \text{ mm}$

A wide-flange (W-shape) beam is used as a tension member in a large truss. It is connected to the joint by bolting only its two flanges to gusset plates; the web is left unconnected. Explain why the effective net area ($A_e$) will be less than the actual net area ($A_n$) and what physical phenomenon this represents.

A W-shape tension member is connected by its flanges only, with 3 bolts per line in the direction of loading. Determine the applicable shear lag factor ($U$) using the simplified shear-lag case applicable to W-shapes in the NSCP Chapter 5 provisions.

A $10 \text{ mm}$ thick steel gusset plate (A36 steel: $F_y = 250 \text{ MPa}, F_u = 400 \text{ MPa}$) is connected to a tension member using a single line of three $20 \text{ mm}$ diameter bolts.

The connection geometry dictates:

• Gross shear area ($A_{gv}$): $2,000 \text{ mm}^2$
• Net shear area ($A_{nv}$): $1,400 \text{ mm}^2$
• Net tension area ($A_{nt}$): $500 \text{ mm}^2$
• Uniform tension stress ($U_{bs}$): $1.0$

Calculate the LRFD design block shear strength ($\phi R_n$) of the gusset plate. Assume $\phi = 0.75$.

An L$100 \times 100 \times 10$ angle ($F_y=250\text{ MPa}, F_u=400\text{ MPa}$) is welded to a gusset plate along its heel and toe. The modeled block path has $A_{gv}=A_{nv}=3000\text{ mm}^2$, $A_{nt}=1000\text{ mm}^2$, and $U_{bs}=1.0$. Determine the LRFD block-shear design strength using $\phi=0.75$.

A design for a heavily loaded tension bracing connection fails the block shear check by $10\%$. The engineer cannot change the thickness of the gusset plate or the size of the member due to architectural constraints. Propose two connection detailing modifications to increase the block shear capacity.

For a candidate block-shear path take $F_y=345\text{ MPa}$, $F_u=450\text{ MPa}$, $A_{gv}=600\text{ mm}^2$, $A_{nv}=500\text{ mm}^2$, $A_{nt}=300\text{ mm}^2$, and $U_{bs}=1.0$. Determine the nominal block-shear strength using the two governing expressions.