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statics tasks 1. In a bridge, a round steel beam rigidly mounted at both ends. The steel beam having a length of exactly 5.00 meter and a diameter of 31.0 mm. The work is carried out at a temperature of + 30 ° C. The outdoor-dimensioned temperature in the winter is - 30 ° C. The maximum allowable tensile stress for steel type = 140 N/mm2 . E-Module = 2.05 ∙ 105 N/mm2 and 𝛼 = 11 ∙10-6 mm /(mm ∙ °C). a) Check whether the tension that occurs in the beam at the coldest dimensioned outdoor temperature can be approved? b) How large tensile force in kN is the beam exposed to in the coldest dimensioned outdoor temperature? 2. A square planar copper slab, which is prevented from expanding in the disc plane, is heated 10 °C. Before the heating, the disc is without tension. E = 1.18 ∙ 105 N /mm2 , v = 0.35 and 𝛼 = 17 ∙ 10-6 per °C. a) What tensions (𝜎x and 𝜎y) arise due to this temperature increase? Help: b) What tensions (𝜎x and 𝜎y) arise if the expansion is prevented only in the xdirection? 3. A cantilever beam of length L = 3 meter and elastic modulus E = 1.18 ∙ 105 N /mm2 exposed to a temperature increase that varies as a function of x: ∆𝑇(𝑥) = 15°C ∙ [1 − ( 𝑥 𝐿 ) 2 ] 𝛼 = 17 ∙ 10−6 𝑝𝑒𝑟 0C a) How longer will the beam extend if it is unobstructed? Help: b) How longer will the beam extract if the extension is limited by a spring with stiffness k = 1.97 ∙ 106 N/mm and A = 50000 mm2 ? Help: The spring force R = k ∙ 𝛿R, when 𝛿R is the abbreviation of the spring. And what is the tension in the beam in this case? c) What is the tension in the beam if the spring is infinitely stiff?

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