University:
Michigan State University
Course:
ERG 100 | Introduction to Engineering Design
Academic year:

2021
Views:

367

Pages:

1
Author:

ilikemyicons0y5

PROBLEM 1.58 A 40-kg platform is attached to the end B of a 50-kg wooden beam AB, which is supported as shown by a pin at A and by a slender steel rod BC with a 12-kN ultimate load. (a) Using the Load and Resistance Factor Design method with a resistance factor φ = 0.90 and load factors γ D = 1.25 and γ L = 1.6, determine the largest load that can be safely placed on the platform. (b) What is the corresponding conventional factor of safety for rod BC ? SOLUTION 3 ΣM A = 0 : (2.4) P − 2.4W1 − 1.2W2 5 5 5 ∴ P = W1 + W 2 3 6 For dead loading, W1 = (40)(9.81) = 392.4 N, W 2 = (50)(9.81) = 490.5 N § PD = ¨ © 5· § (392.4) + ¨ 3¸¹ © For live loading, W1 = mg W2 = 0 From which m = Design criterion. 5· (490.5) = 1.0628 × 103 N 6¸¹ PL = 5 mg 3 3 PL 5 g γ D PD + γ L PL = φ PU PL = φ PU − γ DPD (0.90)(12 × 10 3) − (1.25)(1.0628 × 10 − 3) = γL 1.6 = 5.920 × 103 N (a) m= Allowable load. 3 5.92 × 10 3 5 9.81 m = 362 kg W Conventional factor of safety. P = PD + PL = 1.0628 × 103 + 5.920 × 103 = 6.983 × 103 N (b) F. S. = PU 12 × 103 = P 6.983 × 10 3 F. S . = 1.718 W