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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. |