Two vertical forces are applied to a beam of the cross section shown. Determine the maximum tensile and compressive stresses in portion BC of the beam.
Fig. P4.192
Find the maximum tensile and compressive stress in the portion BC of the beam.
Answer to Problem 192RP
The maximum tensile and compressive stress in the portion BC of the beam are
Explanation of Solution
Given information:
The load P acting on the beam is
Consider the radius of the semi-circular region is
Calculation:
Show the cross-section of the beam as shown in Figure 1.
Refer Figure 1.
The cross-section of the beam consist of a semi-circle 1 and a rectangle 2.
Calculate the area of the semi-circle 1 and a rectangle 2 as follows:
Consider the distance of the centroid of the region 1 and 2 from their bases are denoted by
Calculate the value of the distances
Substitute
Calculate the value of the distances
Substitute
Calculate the distance
Substitute
Calculate the total moment of inertia of the cross-section (I) using the rerlation:
Substitute
Show the forces acting on the beam as shown in Figure 2.
Calculate the value of moment M as follows:
Calculate the stress at the top fiber as follows:
Here,
Calculate the value of
Substitute
Calculate the stress at the top fiber as follows:
Here,
Calculate the value of
Substitute
Thus, the maximum tensile and compressive stress in the portion BC of the beam are
Want to see more full solutions like this?
Chapter 4 Solutions
Mechanics of Materials, 7th Edition
- 4.23arrow_forward5.86 The cast iron inverted T-section supports two concentrated loads of magni- tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d = 48.75 mm and that the moment of inertia of the cross-sectional area about this axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P. 1.0 m 1.0 m 15 mm 3 m 150 mm NA- d 15 mm 150 mm FIG. P5.86arrow_forwardA copper strip (E = 105 GPa) and an aluminum strip (E = 75 GPa) are bonded together to form the composite beam shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N.m, determine the maximum stress in (a) the aluminum strip, (b) the copper strip. Fig. P4.39 Aluminum Copper 24 mm 6 mm 6 mmarrow_forward
- answer 4.4arrow_forwardEXERCISE 4.2 1. Three long parallel wires equal in length are supporting a rigid bar connected at their bottoms as shown in Fig. 4.15. If the cross-sectional area of each wire is 100 mm, calculate the stresses in cach wire. Take E, = 100 GPa and E, = 200 GPa. (Ans. o, 25 MPa ; 0, = 50 MPa] 10 kN Fig. 4.15 Brassarrow_forward4.16 plzarrow_forward
- The couple M is applied to a beam of the cross section shown in a plane forming an angle β with the vertical. Determine the stress at (a) point A, (b) point B, (c) point D.arrow_forward4.19 and 4.20 Knowing that for the extruded beam shown the allowable stress is 120 MPa in tension and 150 MPa in compres- sion, determine the largest couple M that can be applied. 80 mm- 125 mm 54 mm 50 mm 125 mm 40 mm M Fig. P4.20 150 mm Fig. P4.19 Marrow_forwardThe member having a rectangular cross-section, Fig. a, is designed to resist a moment of 40 N # m. In order to increase its strength and rigidity, it is proposed that two small ribs be added at its bottom, Fig. b. Determine the maximum normal stress in the member for both cases.arrow_forward
- Problem 2.35 The 5-ft concrete post is reinforced with six steel bars, each with a 7/8-in. diameter. Knowing that E, = 29 x 106 psi and E.= 3.6 x 106 psi, determine the normal stresses in the steel and in the %3D concrete when a 200-kip axial centric force is applied to the post. 5 ft 10 in. 10 in. Flg. P2.35arrow_forward4.123 plzarrow_forward2.5 m 3.5 m -4.0 m Fig. P2.13arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY