以直杆轴向拉伸为例说明：单元体斜截面上的平衡应力只是保证斜截单元体平衡的应力，不是保证其上质点平衡的应力；单元体平衡与质点平衡是不同的。推导出二向应力状态下质点的平衡应力为σ′_α=(σ²_x+σ²_y+2τ²+2τ(σ²_x+σ²_y)1/2(sinα₂+cosα₂))^1/2，质点平衡应力σ′_α与x轴的夹角为α_x=arctan(τ+(σ²_x+σ²_y)^1/2sin arctan (σ_y/σ_x))/(τ+(σ²_x+σ²_y)1/2cos arctan(σ_y/σ_x))。推导出二向应力状态质点平衡应力的极值条件：σ_x=σ_y；应力σ'_α在与X轴成45°的对角线上；极大值为σ'_α max=2^1/2(σ_x+τ)。推导出质点平衡应力比最大主应力σ₁=σ_x+τ大2^1/2倍。指出σ'_{α max}与σ₁分别发生在两个互相垂直的对角线平面上，且与x轴夹角分别为±45°。 用质点平衡应力建立了新的拉（弯）一剪（扭）组合变形条件σ'_α=(σ² + 2τ²+2στ)^1/2≤ [σ]，它不同于现行 的第三强度理论公式（σ² + 4τ²)^1/2≤ [σ]和第四强度理论公式（σ² + 3τ²)^1/2< [σ];同时，建立了三向应力状 态下第四强度理论的新公式σ'_d= (σ²₁+σ²₂+σ²₃)^1/2≤ [σ],进而推导出正方体被三向等应力拉伸时其最小破坏 应力值为0.58σ_s。它不同于现行的第四强度理论公式σ_xd[ (σ₁-σ₂)²+ (σ₂-σ₃)²+ (σ₃-σ₁)²) /2]^1/2≤ [σ],推翻了正方体被三向等应力拉伸时，无论多大应力都不会被破坏的错误结论。

From the pure extension of the straight bar it can be seen that the balancing stress in the tilted section of the element can only ensure the balance of itself, but can’t ensure the balance of particles on it. The difference between the balance of the element and that of particles on it is demonstrated. A conclusion is drawn that the balancing stress of particles under two dimension stress state is written as σ＇_α = σ^2_x +σ²_y+ 2τ²+2τ（σ²_x+σ²_y）^1/2(sinα₂ + cosα₂))^1/2，and the angle between the direction of the balance stress and axis is written as α_x= arctan ( τ + (σ²_x + σ²_y)^1/2 sin arctan （σ_y/σ_x)) /（τ + （σ²_x+σ²_y）^1/2 cos arctan (σ_y/σ_x)). Under two dimension stress state, the principal stress of element and the maximum balancing stress of particles both take place in the 45°diagonal plane, and the balancing stress of particles is 2^1/2 times that of the principal stress. A new two dimension combining strength condition is derived as σ＇_α = (σ² + 2τ² + 2στ )^1/2≤[σ], and it will replace the formula of bend-torsion combining strength condition of third strength theory ( σ² + 4τ²)^1/2≤[σ] and that of fourth strength theory( σ² + 3τ²)^1/2≤[σ]. A new three dimension combining strength condition is derived as σ＇_d =(σ²₁+σ²₂+σ²₃)^1/2[σ]and can replace the wrong formula σ_xd=[((σ₁ -σ₂)² +(σ₂-σ₃)² +(σ₃-σ₁)²)/2 ]^1/2≤[σ] , which is the corresponding strength formula of the fourth strength theory.