Write expressions of bending moments functions

Assignment Help Mechanical Engineering

Reference no: EM133678297

Problem description

The steel shaft (Vislavidius 2007:24, Fig. 5.1) is subjected to external torques: M_f1 = -320 N.m, M_f2 = -200 N.m, M_f3 = -224N.m, M_f4 = -256N.m, M_f5 = 232 N.m, M_f6 = 768N.m; and consists of 3 parts: a solid cylindrical one (d = 32 mm); a rectangular one (b = 36 mm, h = 54 mm); a tubular one (di = 30 mm, de = 50 mm), as shown in Fig. 7 a.

Draw the diagrams of the internal torques of the maximum shear stresses and of the angles of twist with respect to the cross section No. 1. Shear modulus for steel is G = 80 GPa.

DEFLECTIONS OF BEAMS

Question: Two simple steel beams are acted by the same loading (Vislavidius 2007:31, Table 6.5, diagram No. 5, lengths L₁ = 100 cm,
L₂= 360 cm, L₃ = 300 cm, the force F = 36 kN, the moment M_f = 54 kN.m, and the intensity of the uniformly distributed loading g = 20 kN/m), as shown in Fig. 15 a. The cross section of the first beam is an American standard S-shape, the cross section of the sec¬ond beam is rectangular (Vislavidius 2007:30, Fig. 6.3, b = 65 mm). Elastic modulus of the steel is E = 205 GPa, allowable stress sallow =210MPa.

1. Determine the required standard shape for the first beam.

2. Determine the required depth h for the second beam (dimension h should be divisible by 20 mm, for example, 20, 40,..., 180, 200, 220, ...mm); investigate the stress state at the point K which is in the first (from the left end) section with bending moment and shear force unequal to zero; the position of the point - as shown in Fig. 6.3 [2] (a = 20 mm).

3. Write expressions of bending moments functions for all the segments of the beam and write all the boundary conditions.

4. Determine for the first beam the deflection of the section at the middle of the span and the slope at the left support by the moment-area technique.

Reference no: EM133678297

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