Concept explainers
In the marine crane shown, link CD is known to have a uniform cross section of 50 × 150 mm. For the loading shown, determine the normal stress in the central portion of that link.
Fig. P1.59
The normal stress in the centre portion of the link.
Answer to Problem 59RP
The normal stress in the centre portion of the link is
Explanation of Solution
Given information:
The uniform cross section is
Calculation:
Sketch the free body diagram of ABC as shown in Figure 1.
Here, W is the weight of the loading.
Find the weight of the loading as follows:
Here, m is the mass of the loading and g is the acceleration due to gravity.
Substitute
Taking moment about A,
Substitute
Find the area of the cross section using the relation:
Here, b is the width of the cross section and d is the depth of the cross section.
Substitute
Determine the normal stress in the central portion of the link as follows:
Here, A is the area of the cross section and
Substitute
Thus, the normal stress in the centre portion of the link is
Want to see more full solutions like this?
Chapter 1 Solutions
Mechanics of Materials, 7th Edition
- Two gage marks are placed exactly 250 mm apart on a 12-mm-diameter aluminum rod with E5 73 GPa and an ultimate strength of 140 MPa. Knowing that the distance between the gage marks is 250.28 mm after a load is applied, determine (a) the stress in the rod, (b) the factor of safety.arrow_forwardKnowing that connecting rod BD has a uniform cross section of area equal to 800 mm², determine the magnitude of the load P so that the normal stress in rod BD is 50 MPa.arrow_forwardTwo steel plates are to be held together by means of 16-mm-diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers. Knowing that the average normal stress must not exceed 205 MPa in the bolts and 132 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design. The outer diameter of the spacers that yields the most economical and safe design is mm.arrow_forward
- Straight rods of 0.30-in. diameter and 200-ft length are sometimes used to clear underground conduits of obstructions or to thread wires through a new conduit. The rods are made of high-strength steel and, for storage and transportation, are wrapped on spools of 5-ft diameter. Assuming that the yield strength is not exceeded, determine (a) the maximum stress in a rod, when the rod, which was initially straight, is wrapped on the spool, (b) the corresponding bending moment in the rod. Use E= 29 * 106 psi.arrow_forwardTwo forces P can be applied separately or at the same time to a plate that is welded to a solid circular bar of radius r. Determine the largest compressive stress in the circular bar (a) when both forces are applied, (b) when only one of the forces is applied.arrow_forwardTwo steel plates are to be held together by means of 16-mm-diameter high-strength steel bolts fitting snugly inside cylindrical brass spacers.Knowing that the average normal stress must not exceed 200 MPa in the bolts and 130 MPa in the spacers, determine the outer diameter of the spacers that yields the most economical and safe design.arrow_forward
- a. Determine the normal stress in the element GF if the area is 10 in2, knowing that the load W is 1500lb, express your answer in psi b. determine the normal stress in the element EC if the area is 20 in2arrow_forwardEach of the four vertical Ilinks has an 8 x 36-mm uniform rectangular cross section and each of the four pins has a 16-mm diameter. Take P= 19 kN. 0.4 m C 0.25 m 0.2 m B. P Determine the average bearing stress at Bin member ABC, knowing that this member has a 10 x 50-mm uniform rectangular cross section. MPa. The average bearing stress at Bin member ABC is.arrow_forwardAt a temperature of 32.98 °C a 0.41-mm gap exists between the ends of the rods shown. At a later time when the temperature has reached 131.06°C, determine the magnitude of the normal stress (in MPa) in the steel rod if L = 332.28 mm and M = 209 mm.arrow_forward
- In many situations it is known that the normal stress in a given direc-tion is zero. For example, σz= 0 in the case of the thin plate shown. For this case, which is known as plane stress, show that if the strains εx and εy have been determined experimentally, we can express σx, σyand εz as follows:arrow_forwardA 5.3-m-long steel rod must not stretch more than 2.71 mm and the normal stress must not exceed 181 MPa when the rod is subjected to a 9.99-kNaxial load. Knowing that E = 199.3 GPa, determine the required radius of the rod in mm. Express your answer in four decimal places.arrow_forwardA 5-kN tensile load will be applied to a 50-m length of steel wire with E = 200 GPa. Determine the smallest diameter wire that can be used, knowing that the normal stress must not exceed 150 MPa and that the increase in length of the wire must not exceed 25 mm.arrow_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