A bearing pad is a device which is used to support a bridge or other heavy
structure in a way that permits the load to shift slightly in a horizontal direction
relative to the ground or foundation. If a horizontal force af 528 kN is applied to
the top surface of the bearing pad, and that a = 700 mm, b = 550 mm, h = 75
m and the modulus of elasticity G = 1.25 MPa. Determine the following:
a. The average shear stress on the bearing pad.
b. The horizontal displacemant of tne bearing pad.
Note: Draw the Free Body Diagram, include the proper units and round-off the answers to 3 decimal places.
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Extracted text: Fundamental Equations of Mechanics of Materials Axial Load Shear Normal Stress Average direct shear stress V A Tavg A Displacement P(x)dx Transverse shear stress 8 = A (x)E VQ It PL AE Shear flow VQ q = Tt = δ- α ΔΤL = a Torsion Stress in Thin-Walled Pressure Vessel Shear stress in circular shaft Тр Cylinder pr pr 2t where Sphere pr = solid cross section 01 = 02 = 2t J = - (c,“ – c,") Stress Transformation Equations tubular cross section 0x + 0y O, – 0, + y cos 20 + Power sin 20 2 P = Tw = 2™fT Ox – 0y Angle of twist sin 20 + Try cos 20 2 T(x)dx Principal Stress J(x)G Txy tan 26, TL $ = E JG (ox – 0,)/2 Ox + 0y 1,2 0,- 0, y Average shear stress in a thin-walled tube + Tây 2 T Tavg 21A m Maximum in-plane shear stress (0, – 0,)/2 Shear Flow tan 20, T Txy q = Tavg! 2A m Tmax + Txy 2 Bending Ox + 0y O avg Normal stress Мy Absolute maximum shear stress I σ. max Unsymmetric bending Tabs max for ởmax, O min same sign 2 Mạy max Ở min tan a Tabs max for omax, Omin Opposite signs tan 0 2 Geometric Properties of Area Elements Material Property Relations Poisson's ratio -A = bh Elat 1, = bh !, = hb long C %3D Generalized Hooke's Law :[0, - vo, + o.)] Rectangular area %3D Ex E [0, – v(o, + 0,)] -A = bh E Ez [0. - v(0, + 0,)] E 1 Tyz, Yzx 1 %3D Yxy Txy Yyz Triangular area where E G = 2(1 + v) A = a (9 + D)w : Relations Between w, V, M h (2a + b\ a + b dM = V dx dV b w(x), dx Trapezoidal area Elastic Curve 1 M -A = EI d*v EI =w(x) !, = }ar* %3D d'v El = V(x) Semicircular area dv El dx? M(x) -A = Tr² Buckling Critical axial load 1, = fart !, = fart T²EI Per (KL)² Critical stress VIJA O cr Circular area (KL/r)²* Secant formula ес P Ở max 1 + sec A V EA žab A = Energy Methods Conservation of energy U. = U; zero slope Strain energy N²L Semiparabolic area U; = 2AE constant axial load "M²dx U, = bending moment %3D 2EI A = U; = transverse shear %3D 2GA zero slope - pLT°dx torsional moment %3D 2GJ Exparabolic area