Home Rationale Specifications Drawings Electronics Beam Calculations Beam Test Data Earthquake Data Quake News Article Calculate tilt of Zerodur beam supported at ends, centrally loaded, given: L = unsupported beam length = 400 mm       total length is 500 mm, supports 50 mm from ends b = beam width = 100 mm h = beam height = 24.7 mm E = Modulus of elasticity = 9.03x1010 Pa = 9.03x104 N/mm2 I = Moment of Inertia = b*h3/12 = 1.26x105 mm4 EI = (9.03x104*1.26x105) = 1.13x1010 N mm2 Z = Section Modulus = I/(h/2) = 1.02x104 mm3 W = central load = 0.5 Kg = 4.9 N/mm2 x = point coordinate relative to support Y(x) = deflection = (Wx/48EI)(3L2 - 4x2) S(x) = extreme fiber stress = -Wx/2Z Calculate central deflection and stress: x = L/2 Ycent =  Ymax = Y(L/2) = WL3/48EI= (4.90*4003)/(48*1.13x1010) = 580 nm                              See Beam Test Data 2 in good agreement Scent = Smax = -WL/4Z= -(4.90*400)/(4*1.02x104) = .048 N/mm2 = 5x103 Pa The Schott web site lists bending strengths for bonded Zerodur pieces in the range of 25 to 50 MPa; an older Schott publication listed Zerodur bending strengths of 70 to 120 MPa depending on surface finish. Tilt = T = dY/dx = d/dx[(W/48EI)(3xL2-4x3)] = [W/16EI](L2 - 4x2)                  with max at supports, minimum at center  Tmax = T(0) = WL2/16EI = (4.90*4002)/(16*1.13x1010)= 4.3 microradians Tcent = T(L/2) = 0 See Beam Test Data 1, in good agreement.