104年 - 104 國立嘉義大學_碩士班(甲組)招生考試試題_土木與水資源工程學系：材料力學#146078

科目：研究所、轉學考(插大)◆材料力學 | 年份：104年 | 選擇題數：0 | 申論題數：9

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所屬科目：研究所、轉學考(插大)◆材料力學

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申論題 (9)

1. Determine the shear force and bending moment diagrams for the beam in Fig. 1. (20%)
Fig. 1
2. A prismatic bar is suspended from the ceiling and loaded only by its own weight. If the unloaded bar has length L, cross-sectional area A, weight density r, and modulus of elasticity E, what is its length when suspended? (20%)
3. A pressurized steel tank is constructed with a helical weld that makes an angle α = 55° with the longitudinal axis (Fig. 2). The tank has radius r = 0.6 m, wall thickness t = 18 mm, and internal pressure p = 2.8 MPa. Also, the steel has modulus of elasticity E = 200 GPa and Poisson’s ratio = 0.30. Determine the following quantities for the cylindrical part of the tank.
(a)The circumferential and longitudinal stresses.
(b)The maximum in-plane and out-of-plane shear stresses.
(c)The circumferential and longitudinal strains.
(d)The normal and shear stresses acting on planes parallel and perpendicular to the weld (show these stresses on a properly oriented stress element). (20%)
Fig. 2



4. An overhanging beam ABC has a guided support at A, a rectangular cross section, and supports an upward uniform load q = P/L over AB and a downward concentrated load P at the free end C (Fig. 3). The span length from A to B is L, and the length of the overhang is L/2. The cross section has width b and height h. Point D is located midway between the supports at a distance d from the top face of the beam. Knowing that the maximum tensile stress (principal stress) at point D is σ1 = 38 MPa, determine the magnitude of the load P. Data for the beam are as follows: L = 1.75 m, b = 50 mm, h = 220 mm, and d = 55 mm. (20%)
Fig. 3
5. An element in pure shear is subjected to stresses τxy = 26 MPa, as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an element oriented at a slope of 3 on 4
(Fig. 4).
(b) The principal stresses. Show these stresses on sketches of properly oriented elements. (20%)