Engineering Asked by York Tsang on May 6, 2021
According to clause 4.8.3.2 the cross-section capacity for non-slender section is:
$$frac{F_c}{A_g p_y}+frac{M_x}{M_{cx}}+frac{M_y}{M_{cy}}leq 1 qquad (1)$$
According to clause 4.8.3.3.1 simplified method of member buckling resistance, the following relationship should be satisfied:
$$frac{F_c}{P_c}+frac{m_x M_x}{p_y Z_x}+frac{m_y M_y}{p_y Z_y}leq 1quad (2)$$
Let’s consider a beam-column with class 1 section (doubly-symmetric) under uniform moment (so that the equivalent moment factor $m_x = m_y =1$ according to Table 26) and axial compression, and ignore lateral-torsional buckling. In this case, equation (2) is always critical than equation (1), because $P_c leq A_g p_y$ and $p_y Z_x leq M_{cx}$, $p_y Z_y leq M_{cy}$.
My questions are:
I understand that the simplified method is at the cost of conservatism, but making one criterion obsolete seems too much to me.
Thank you for your time.
Edit 1:
For stocky columns, material yielding and ultimate failure will come before even reaching the buckling load.
Just think about Euler's equation:
$$P_{cr} = dfrac{pi^2 EI}{L_{cr}^2}$$
If $L_{cr} rightarrow 0$ then $P_{cr} rightarrow infty$.
Hence, equation one can be more critical and $P_{cr}$ can be greater than $Af_y$.
Answered by Apostolos Grammatopoulos on May 6, 2021
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