Beam, uniformly loaded

Example.—The general equation for the deflection of a horizontal beam uniformly loaded and subjected to the pressure of its supports is. ... 

The shell of a column-supported tank, vessel, or bin is considered to be a circular girder or ring beam uniformly loaded over its periphery and supported by columns equally spaced on the ring circumference. 

Condition (1) applies to cantilever beams and to simple beams uniformly loaded, or with equal concentrated loads placed at equal distances from the center of the beam. In the cantilever beam, the reaction is the sum of all the vertical forces acting downward, comprising the weight of the beam and the superposed loads. In the simple beam each reaction is equal to one-half the total load, consisting of the weight of the beam and the superposed loads. Condition (2) applies to a simple beam not uniformly loaded. The reactions are computed separately, by determining the moment of the several loads about each support. The sum of the moments of the load around one support is equal to the moment of the reaction of the other support around the first support. 

UpOfOliMLY Loaoed Beams with Free Ends. Refeiring to Fig. 4.10, consider any p<)int, x, between supports / i ftpd / 2 in the beam uniformly loaded with ti> pounds linear inch. The forces acting on the beam to the left of MBt X produce a bC nding moment, M, which can be evaluated by a summation of t he moments at a. For a uniformly loaded beam freely supported at the ends, Ri = R% therefore... 

The first condition applies to cantilever beams and to simple beams uniformly loaded, or with equal concentrated loads placed at equal... 

SIMPLY SUPPORTED BEAM UNIFORMLY DISTRIBUTED LOAD... 

Wind loading will only be important on tall columns installed in the open. Columns and chimney-stacks are usually free standing, mounted on skirt supports, and not attached to structural steel work. Under these conditions the vessel under wind loading acts as a cantilever beam, Figure 13.19. For a uniformly loaded cantilever the bending moment at any plane is given by ... 

A vessel supported on two saddles can be considered as a simply supported beam, with an essentially uniform load, and the distribution of longitudinal axial bending moment will be as shown in Figure 13.22. Maxima occur at the supports and at mid-span. The... 

The first step in developing a resistance function is to determine the plastic section capacities, such as plastic moment, Mp, as shown in Figure 7.1. The next step is to determine the sequence of plastic hinge formation and the corresponding load and deformation values. This is done by incrementally applying loads until a collapse mechanism is formed as illustrated in Figure 7.2 for a fixed end beam with a uniform load. 

Distributed Load—If the pressure is distributed over a beam of length 2b and unit width, as shown in Figure 43, with a uniform loading of P0 per unit length, then the stress intensity pz at any point (x, z) is given by either of the equations ... 

A vessel supported on two saddles can be considered as a simply supported beam, with an essentially uniform load, and the distribution of longitudinal axial bending moment will be as shown in Figure 13.22. Maxima occur at the supports and at mid-span. The theoretical optimum position of the supports to give the least maximum bending moment will be the position at which the maxima at the supports and at mid-span are equal in magnitude. For a uniformly loaded beam the position will be at 21 per cent of the span, in from each end. The saddle supports for a vessel will usually be located nearer the ends than this value, to make use of the stiffening effect of the ends. 

Determine the shape of a single cantilevered beam, whose material behavior in tension is that of a viscoelastic standard solid, under a load P applied at its free end and a uniform load P per unit length of the beam (see Fig. P17.2.1). 

The programme was developed for a simply supported bipartite beam (Fig. 8). It can calculate a uniform load q (kN/m), which is a common case in engineering practice. It can also calculate two symmetrically placed point loads, which correspond to the beam test set-up which is later described in Section 5. The calculation results could, therefore, be directly compared to the actual test results. The modulus of elasticity of the wood was E. The beam span was L, and the width b. The height of the bipartite beam comprises hi for the upper member and h2 for the bottom member, with the total height being h = hi+h2. 

It can readily be shown (reference 10,) that the support rotation capacity of a uniformly loaded simply supported beam needs to be 13 mrad to meet the serviceability limit state of a maximum deflection l/250th of the beam span. Note that this rotation assumes the beam is attached to rigid columns and that it is therefore not necessarily the situation at external connections or at internal connections subjected to non symmetric deformation. 

The lowest for a bolted major-axis connection was 20 mrad. However, it is seen in Figures 4 to 6 that the rotation can be higher than this without a connection failing. To ensure that a serviceabihty limit state is reached before an ultimate one, the ultimate connection rotation can be taken to be 25 mrad. This corresponds to a deflection limit of l/128th of the span for a simply supported beam with uniform loading. The argument for this proposal is developed in reference 10. 

Recommendations (1) to (6) are for major-axis and (7) and (8) are for minor-axis connections. The beam is assumed to have rigid supports and vertical uniform loading only. 

Example 10-7 A floor has a uniformly distributed load of 150 Ib/ft. Floor joists are 18 ft long and spaced 2 ft on center. What is the load on one joist Ignore dead loads. If each end of each joist rests on a beam, what load does each joist transfer to a beam on each of its ends ... 

Calculate the area supported by each beam and multiply this area times the uniform load to get the load supported by each beam. 

K = End connection coefficient per AISC Ki = Vertical distance from bottom of beam flange to top of fillet on web, in LL = Live load. Lbs M = Moment, in-Lbs nb = Number of bolts required Ug = Number of bearing bars per foot Nb = Minimum bearing length, in N = Number of beams P = Concentrated load. Lbs PL = Product load. Lbs Pc = Free area in packing/catalyst, % p = Uniform load over entire bed, PSI r = Radius of gyration, in R = End reactions, Lbs Ra = Root area of bolt, in ... 

UNIFORM LOADD UE TO BEAM WEIGHT UNIFORM LOAD DL a E TO BEAM WEIGHT... 

In the hub ring design the radial beams are typically one quarter of the vessel diameter in length. Since the moment formula for a simply supported, uniformly loaded beam is wl /8, the beams are proportional, not to... 

The estimation of the settlement of the slab in the softened clay area is determined by considering the consolidated clays as a simply supported beam subjected to a uniform load (figure 5). 

Beam fixed at both ends, uniform load per unit length... 

Figure 14. Idealized force-displacement curve resulting from a fracture experiment using a uniform double cantilever beam specimen. Load is applied to a certain displacement until the crack propagates, at which point the load and crack length are measured. The diagram shows the results of an experiment in which the sample is unloaded prior to reloading. The change in slope with each reloading is due to the change in compliance of the specimen which is a function of crack length.

We can now draw graphs that allow the determination of the first natural frequency of uniformly loaded beams with = 0,44. 

Rg. 2.2. Forces on on efemeni of o uniformly loaded beam, (o) Uni fcrmly loaded beam, (b) Deloit of element dx. 

Uniformly Loaded Continuous Beam. A unifonnly loaded continuous beam having a large number of e((ually Sj teed supports reacts the sa p as a simple uiufomily teite beam with fixed ends. Cion.sider tli uniformly loaded beam shown in Fig. 4.11. The beam is assumed to be a section of a txMilinuous Iw.am with a large number of equally spaced f distonces apart. A beading... 

Solving for the product yc for the uniformly loaded beam, we obtain ... 

The stresses produced in a self-supporting vertical vessel by the action of the wind are calculated by con dering the vessel to 1 a verticle, uniformly loaded cantilever beam. The wind loading is a function of the wind veloirfty, air density, and the shape of the tower. The Unip States Weather Bureau (137) has correlated Uie above factors in the following relation ... 

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