Final answer:
To find the most economical 20' tall W14 beam column, we need to compare the axial and bending capacities of each option. Based on this comparison, the most economical choice is the W14x311.
Step-by-step explanation:
To determine the most economical 20' tall W14 beam column to carry the given load, we need to check the axial and bending capacities of each option. A992 steel columns are commonly used for structural applications, and their properties can be found in engineering handbooks or online resources.
To check axial capacity, we need to compare the factored load (500k) with the compression strength of each column. The axial capacity is determined by the cross-sectional area of the column. The W14x90 has the smallest cross-sectional area, so it can be ruled out. To check the bending capacity, we need to compare the bending moments (200 ft-kips and 100 ft-kips) with the moment of inertia and section modulus of each option. The W14x311 has the highest moment of inertia and section modulus, making it capable of carrying the bending loads.
Therefore, based on the axial and bending capacity, the most economical option would be the W14x311.