钢梁弯扭屈曲临界弯矩通用公式研究

为研究钢梁弯扭屈曲总势能方程中的各势能项对临界弯矩M_cr通用公式中各系数取值的影响，由总势能方程推导临界弯矩M_cr的通用公式及3种典型总势能方程下各系数的计算式，揭示各势能项与各个系数的联系，计算无侧向支撑简支钢梁临界弯矩M_cr通用公式中各系数的数值，并分别分析现行国家标准GB 50018-2002和GB 50017-2003的整体稳定系数φ_b设计公式存在取值各异的问题。结果表明：系数C₁、C₂和C₃的取值除都与非线性正应变能和非线性剪应变能有关外，系数C₁的取值还与圣维南扭转应变能有关，系数C₂的取值还与外荷载势能有关，而影响系数C₃取值的势能项则因总势能方程而异；现行国家标准GB 50018-2002和GB 50017-2003的φ_b设计公式应采用统一的形式，且应统一φ_b设计公式中系数C₃的取值。

Study on general formula of critical moment of steel beam with flexural-torsional buckling

In order to study how each potential energy in total potential energy equation influences the value of coefficients in the general formula of critical momentM_cr ,the general formula of M_cr and the formula of its coefficients were derived based on three typical total potential energy equations respectively, and the relationship between each potential energy and the coefficients was pointed out. Based on the series of formulas derived in this paper, the values of the coefficients for a simply supported steel beam without lateral support were calculated, and the defects of overall stability factor φ_b in current national standards GB 50018-2002 and GB 50017-2003 were analyzed. The conclusions show that except for nonlinear normal strain energy and nonlinear shear strain energy, the value of coefficient C₁ is influenced by Saint-Venant torsional strain energy and the value of coefficient C₂ is influenced by potential energy of loads. However the potential energy which influences the value of coefficient C₃ is varied from different total potential energy equations. The design formula of overall stability factor φ_b in current national standards GB 50018-2002 and GB 50017-2003 should be in unified form and the value of coefficient C₃ should also be unified.