end pin supported beam has the cross-se
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- Obtain a formula for the ratio c/maxof the deflection at the midpoint to the maximum deflection for a simple beam supporting a concentrated load P (see figure). From the formula, plot a graph of c/max versus the ratio a/L that defines the position of the load (0.5 < a/L < ) What conclusion do you draw from the graph? (Use the formulas of Example 9-3.)A simple beam AB of length L is subjected to loads that produce a symmetric deflection curve with maximum deflection S at the midpoint of the span (see figure). How much strain energy U is stored in the beam if the deflection curve is (a) a parabola and (b) a half wave of a sine curve?A cantilever beam AB with a circular cross section and length L = 750 mm supports a load P = 800 N acting at the free end (see figure). The beam is made of steel with an allowable bending stress of 120 MPa. Determine the required diameter dmm(figure part a) of the beam, considering the effect of the beam's own weight. Repeat part (a) if the beam is hollow with wall thickness t = df$ (figure part b); compare the cross-sectional areas of the two designs.
- -5-7 A cantilever beam AB carries three equalaly spaced concentrated loads, as shown in the figure. Obtain formulas for the angle of rotation B and deflaction B at the free end of the beam.A beam ABC is fixed at end A and supported by beam DE at point B (sec figure). Both beams have the same cross section and are made of the same material. Determine all reactions due to the load P. What is the numerically largest bending moment in cither beam?What is the span length L of a uniformly loaded, simple beam of wide-flange cross section (see figure) if the maximum bending stress is 12,000 psi, the maximum deflection is 0.1 in., the height of the beam is 12 in., and the modulus of elasticity is 30 × 106psi? (Use the formulas of Example 9-1.)
- A two-axle carriage that is part of an over head traveling crane in a testing laboratory moves slowly across a simple beam AB (sec figure). The load transmitted to the beam from the front axle is 2200 lb and from the rear axle is 3800 lb. The weight of the beam itself may be disregarded. Determine the minimum required section modulus S for the beam if the allowable bending stress is 17,0 ksi, the length of the beam is 18 ft, and the wheelbase of the carriage is 5 ft. Select the most economical I-beam (S shape) from Table F-2(a), Appendix F.A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, Labeling all critical ordinales.A simply supported wooden I-beam with a 12-ft span supports a distributed load of intensity q = 90 lb/ft over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web, as shown in the figure part b. The plywood is 3/8 in. thick: the flanges are 2 in, × 2 in, (actual size). The modulus of elasticity for the plywood is 1,600,000 psi and for the pine is 1,200,000 psL Calculate the maximum bending stresses in the pine flanges and in the plywood web. What is q, if allowable stresses are 1600 psi in the flanges and 1200 psi in the web?
- Two wood beams, each of rectangular cross section (3.0 in. x 4.0 in., actual dimensions), are glued together to form a solid beam with dimensions 6.0 in. x 4.0 in. (sec figure). The beam is simply supported with a span of S ft. What is the maximum moment Mmaxthat may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beams own weight, assuming that the wood weighs 35 lb/ft3.) Repeat part (a) if Mmaxis based on allowable bending stress of 2500 psi.A cantilever beam model is often used to represent micro-clectrical-mechanical systems (MEMS) (sec figure}. The cantilever beam is made of polysilicon (E = 150 GPa) and is subjected to an electrostatic moment M applied at the end of the cantilever beam. 1 f dimensions arc h — 2 [im, h — 4 ^m, and L = 520 ^mt find expressions for the tip deflection and rotation of the cantilever beam in terms of moment M.A simple beam AB is loaded as shown in the figure. Calculate the required section modulus S if ^aibw = IS,000 psi, L = 32 ft, P = 2900 lb, and g = 450 lb/ft. Then select a suitable I-beam (S shape) from Table F-2(a), Appendix F, and recalculate 5 taking into account the weight of the beam. Select a new beam size if necessary. What is the maximum load P that can be applied to your final beam selection in part (a)?