(a) Explanation Given information: The width ( b ) and depth ( D ) of the cross-section of the beam are 3 4 in . and 4.5 in . . Consider the depth of the beam near the radius of the semicircular grooves is denoted by d . The bending stress M for beam is 4 kip ⋅ in . . The radius r of the semicircular grooves is 3 8 in . . Calculation: Calculate the depth d using the relation: d = D − 2 r (1) Substitute 4.5 in . for D and 3 8 in . for r in Equation (1). d = 4.5 in . − 2 × 3 8 in . = 4.5 in . − 0.75 in . = 3.75 in . Calculate the moment of inertia ( I ) of the cross section of the beam using the relation: I = 1 12 b d 3 (2) Here, b and d are the cross sectional width and depth of the beam. Substitute 3 4 in . for b and 3.75 in . for d in Equation (2). I = 1 12 × 3 4 × 3.75 3 = 158.20 48 = 3.296 in . 4 Consider the distance between the neutral axis and the extreme outer fiber is denoted by c . Calculate the distance c using the relation: c = d 2 (3) Substitute 3 (b) To determine The maximum stress M in the beam, when the radius of the semicircular grooves is 3 4 in .

7th Edition

ISBN: 8220100257063

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 4.5, Problem 64P

(a)

To determine

The maximum stress in the beam, when the radius of the semicircular grooves is 38 in.

(b)

To determine

The maximum stress M in the beam, when the radius of the semicircular grooves is 34 in.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 63P

Chapter 4.5, Problem 65P

Students have asked these similar questions

A cast-iron machine part is acted upon by the 3 kN-m couple shown. Know-ing that E= 165 GPa and neglecting the effect of fillets, determine (a) the maximum tensile and compressive stresses in the casting and (b) the radius of curvature of the casting

M = 500 Nm PROBLEM 4.2 В Knowing that the couple shown acts in the vertical plane, determine the stress at (a) point A, and (b) point B. [Ans. (a) -116.4 MPa (b) -87.3 MPa] 30 mm 40 mm Fig. P4.2

Prob.4: [2.37] The 1.5 m concrete post is reinforced with six steel bars, each with 28 mm diameter. Knowing the E, = 200 GPa and Ec = 200 GPa, determine the normal stresses in the steel and concrete when a 1550 kN axial centric force P is applied to the post. 450 mm 1.5 m

Chapter 4 Solutions

EBK MECHANICS OF MATERIALS

Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - Using an allowable stress of 155 MPa, determine...Ch. 4.3 - Solve Prob. 4.3, assuming that the wide-flange...Ch. 4.3 - Using an allowable stress of 16 ksi, determine the...Ch. 4.3 - Knowing that the couple shown acts in a vertical...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The maximum stress in the beam, when the radius of the semicircular grooves is 3 8 in .

Solution Summary: The author explains the maximum stress in the beam, when the radius of the semicircular grooves is 38