[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-impact-dynamic-factor":3},{"formula":4,"related_topics":12,"alternates":21},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},113,"impact-dynamic-factor","Dynamic Factor for Vertical Impact","δmax = δst + √(δst² + 2hδst)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For an idealized linearly elastic system without energy losses, when a weight falls from height $h$ and then deforms the structure, the maximum displacement can be expressed through the static displacement $\\delta_{st}$ caused by the same weight $P$:\u003C\u002Fp>\u003Cp>$$\\delta_{max}=K_d\\delta_{st},$$\u003C\u002Fp>\u003Cp>where the dynamic factor is:\u003C\u002Fp>\u003Cp>$$K_d=1+\\sqrt{1+\\frac{2h}{\\delta_{st}}}.$$\u003C\u002Fp>\u003Cp>If stresses in the linear system are proportional to load:\u003C\u002Fp>\u003Cp>$$\\sigma_{dyn}=K_d\\sigma_{st}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$P$\u003C\u002Fstrong> — weight acting as the reference static force;\u003C\u002Fli>\u003Cli>\u003Cstrong>$h$\u003C\u002Fstrong> — drop height;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\delta_{st}$\u003C\u002Fstrong> — static displacement under $P$;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\delta_{max}$\u003C\u002Fstrong> — maximum displacement during impact;\u003C\u002Fli>\u003Cli>\u003Cstrong>$K_d$\u003C\u002Fstrong> — dynamic factor;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\sigma_{st}$, $\\sigma_{dyn}$\u003C\u002Fstrong> — static and maximum dynamic stresses.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>For suddenly applied loading with zero initial velocity, $h=0$ and therefore $K_d=2$. The formula assumes elastic behavior, negligible energy loss, and a correctly determined static compliance in the impact direction.\u003C\u002Fp>\u003Cp>Because $K_d$ is dimensionless and has no separate quantity in the registry, the calculator uses the equivalent displacement relation without treating $K_d$ as a variable.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17],{"id":14,"name":15,"path":16},75,"Dynamic and Cyclic Loading","strength-of-materials\u002Fdynamic-and-cyclic-loading",{"id":18,"name":19,"path":20},77,"Impact Loading Calculations","strength-of-materials\u002Fdynamic-and-cyclic-loading\u002Fimpact-loading-calculations",{"en":22,"uk":23},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Fimpact-dynamic-factor","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fimpact-dynamic-factor",1787712544112]