Question 1: (Section 6.4 - Doubly Symmetric Beams with Inclined Loads) [45 points] A 4 meter ong wide-flange HE450A I-be

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Question 1 Section 6 4 Doubly Symmetric Beams With Inclined Loads 45 Points A 4 Meter Ong Wide Flange He450a I Be 1 (80.5 KiB) Viewed 36 times

Question 1: (Section 6.4 - Doubly Symmetric Beams with Inclined Loads) [45 points] A 4 meter ong wide-flange HE450A I-beam in Figure 1 (a and b) is simply supported and carries a oad P of 45 kN. The load P is applied on the centroid C located at mid-span of the beam. The supports on which the beam is attached are inclined at a slope of 1:2, with the angle a. Because the beam is very narrow compared to its height, its moment of inertia about the z-axis is much arger than its moment of inertia about the y-axis. You are tasked to conduct structural bending analysis of the beam, to estab ish the effect of the load and its direction of application on the beam. You are therefore required to determine: (i) The maximum bending stress Omax of the beam, if the y-axis of the beam is vertical and perfectly aligned with the load P as seen in Figure 1a. [6] (ii) The orientation of the neutral axis, in Figure 1b. [6] (ii) The maximum normal stresses at the outside corners (A, B, D and E) of the beam cross section in Figure 1b. [33] Assumptions: • The load P is acting in a plane of symmetry. • Both the x-y and the x-z planes are planes of symmetry. • The neutral axis is an axis of symmetry of the cross section, hence the maximum tensile and compressive bending stresses are equal in magnitude and occur at the region of the argest bending moment. D E C B 3 P Figure 1 (a) (b)