Ch.1 Problem 1.36 Solution - Edubirdie

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

2021
Views:

274

Pages:

1
Author:

Hallie Randolph

PROBLEM 1.36 A centric load P is applied to the granite block shown. Knowing that the resulting maximum value of the shearing stress in the block is 18 MPa, determine (a) the magnitude of P, (b) the orientation of the surface on which the maximum shearing stress occurs, (c) the normal stress exerted on that surface, (d) the maximum value of the normal stress in the block. SOLUTION A0 = (140 mm)(140 mm) = 19.6 × 10 3mm 2 = 19.6 × 10 −3m 2 τ max = 18 MPa = 18 × 10 6 Pa θ = 45 ° for plane of τmax (a) Magnitude of P. τ max = |P| so P = 2 A 0 τ max 2A 0 P = (2)(19.6 × 10− 3)(18 × 10 6) = 705.6 × 10 3N sin 2θ is maximum when 2θ = 90° (b) Orientation. (c) Normal stress at θ = 45°. σ = (d) P = 706 kN W θ = 45° W Pcos 2 θ (705.8 × 10 3) cos 2 45 ° = = 18.00 × 10 6Pa − A0 19.6 × 10 3 Maximum normal stress: σ max = σ max = σ = 18.00 MPa W P A0 705.8 × 103 19.6 × 10 −3 = 36.0 × 106 Pa σ max = 36.0 MPa (compression) W

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