![]() ![]() ![]() The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. Objects at equilibrium (the condition in which all forces balance) will not accelerate. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. The dimensions of (\w\) are force per length.Newton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The distribution is of trapezoidal shape, with maximum magnitude w at the interior of the beam, while at its two ends it becomes zero. This load distribution is typical for the beams in the perimeter of a slab. Simply supported beam with slab-type trapezoidal load distribution Simply supported beam with uniform distributed load (UDL) In the following table, the formulas describing the static response of the simple beam under a uniform distributed load w are presented. Either the total force W or the distributed force per length w may be given, depending on the circumstances. The total amount of force applied to the beam is W=w L, where L the span length. ![]() The load w is distributed throughout the beam span, having constant magnitude and direction. Simply supported beam with uniform distributed load I : the moment of inertia of the cross-section around the elastic neutral axis of bending.E : the material modulus of elasticity (Young's modulus).A different set of rules, if followed consistently would also produce the same physical results. These rules, though not mandatory, are rather universal. The bending moment is positive when it causes tension to the lower fiber of the beam and compression to the top fiber.The shear force is positive when it causes a clock-wise rotation of the part.The axial force is considered positive when it causes tension to the part.Sign conventionįor the calculation of the internal forces and moments, at any section cut of the beam, a sign convention is necessary. The last two assumptions satisfy the kinematic requirements for the Euler Bernoulli beam theory that is adopted here too. This is the case when the cross-section height is quite smaller than the beam length (10 times or more) and also the cross-section is not multi layered (not a sandwich type section). Every cross-section that initially is plane and also normal to the longitudinal axis, remains plane and and normal to the deflected axis too. ![]()
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