Module 8: Steel Beams (Flexural Members) - Examples & Applications

Determine the plastic moment benchmark ($M_p$) of a W16x36 beam of A992 steel ($F_y = 345 \text{ MPa}$). Then interpret what additional conditions must be satisfied before $M_p$ can govern nominal flexural strength.

Given Section Properties:

• Plastic Section Modulus ($Z_x$): $1.05 \times 10^6 \text{ mm}^3$

Determine the LRFD design flexural strength ($\phi_b M_n$) of the same W16x36 beam ($M_p = 362.25 \text{ kN}\cdot\text{m}$). Assume the compact section is connected to a concrete floor system that provides the effective continuous lateral restraint required by the design model.

LRFD Factor: $\phi_b = 0.90$ for flexure.

Determine the nominal moment capacity ($M_n$) of a W14x90 beam of A992 steel ($F_y = 345 \text{ MPa}$) with an unbraced length $L_b = 6.0 \text{ m}$. Assume the moment gradient yields a bending coefficient $C_b = 1.14$.

Given Section Properties and Limits:

• Plastic Moment ($M_p$): $600 \text{ kN}\cdot\text{m}$
• Yield Moment modified for residual stress ($0.7 F_y S_x$): $420 \text{ kN}\cdot\text{m}$
• Limiting unbraced length for plastic yielding ($L_p$): $4.0 \text{ m}$
• Limiting unbraced length for inelastic buckling ($L_r$): $12.0 \text{ m}$

An engineer designs a roof using standard W-shape steel beams spaced 3 meters apart. Initially, the metal roof deck was planned to be directly fastened to the top flanges of the beams, providing continuous lateral support. However, to save money, the contractor proposes removing the direct fastening and only bracing the beams at their ends (12 meters apart). Explain the structural consequences of this change regarding the beam's moment capacity.

A W24x68 steel beam ($F_y=345\text{ MPa}$) has a maximum factored shear $V_u=450\text{ kN}$. For the stated worked case, take $C_v=1.0$ and $\phi_v=1.00$.

A simply supported floor beam spans $8.0 \text{ meters}$. Under service (unfactored) loads, the immediate elastic deflections are calculated as: $\Delta_{\text{Dead}} = 12 \text{ mm}$ and $\Delta_{\text{Live}} = 18 \text{ mm}$. For this worked example, the project serviceability criteria specify a live-load limit of $L/360$ and a total-load limit of $L/240$.

Verify if the beam satisfies serviceability requirements.

A W14x90 column is subjected to factored axial compression $P_u=1200\text{ kN}$ and factored major-axis moment $M_{ux}=250\text{ kN}\cdot\text{m}$. The supplied available strengths are $\phi_cP_n=3000\text{ kN}$ and $\phi_bM_{nx}=550\text{ kN}\cdot\text{m}$, with no y-axis moment. Evaluate the stated NSCP Section 508 interaction check.

A compact steel beam is controlled by lateral-torsional buckling. The architecture permits a credible brace at midspan. What structural change should be evaluated before selecting a heavier beam?

For a compact doubly symmetric I-shape take $F_y=345\text{ MPa}$, $E=200{,}000\text{ MPa}$, and $r_y=40\text{ mm}$. The quarter-point absolute moments in one unbraced segment are $M_A=80$, $M_B=60$, $M_C=40\text{ kN}\cdot\text{m}$ and $M_{max}=100\text{ kN}\cdot\text{m}$.

For a stated unstiffened web case, take $h/t_w=150$, $k_v=5.0$, $E=200{,}000\text{ MPa}$, $F_y=345\text{ MPa}$, overall depth $d=600\text{ mm}$, and $t_w=4\text{ mm}$. Determine $C_v$, $V_n$, and the LRFD available shear strength using $\phi_v=0.90$ for this non-special G2 case.