Concept explainers
Two cover plates, each 7.5 mm thick, are welded to a W460 × 74 beam as shown. Knowing that σall = 150 MPa for both the beam and the plates, determine the required value of (a) the length of the plates, (b) the width of the plates.
Fig. P5.144 and P5.145
(a)
Find the length of the plates.
Answer to Problem 145P
The length of the plates is
Explanation of Solution
The length of the cover plate is
The thickness of the cover plate is
The width of the cover plate is
The allowable normal stress in the beam is
Show the free-body diagram of the prismatic beam as in Figure 1.
Determine the vertical reaction at point B by taking moment at point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Show the free-body diagram of the section AD as in Figure 2.
Determine the moment at point D by taking moment about point D.
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The section modulus of the
Determine the moment at point D
Here, the allowable stress of the beam is
Substitute 150 MPa for
Find the length of the plate using trial and error method.
Therefore, the length of the plates is
(b)
Find the width of the plates.
Answer to Problem 145P
The width of the plates is
Explanation of Solution
The length of the cover plate is
The thickness of the cover plate is
The width of the cover plate is
The allowable normal stress in the beam is
Show the free-body diagram of the prismatic beam as in Figure 3.
Determine the vertical reaction at point B by taking moment at point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Show the free-body diagram of the section AC as in Figure 4.
Determine the moment at point C by taking moment about point C.
Show the cross section of the beam as in Figure 5.
Determine the section modulus (S) of the beam using the relation.
Here, the allowable normal stress in the beam is
Substitute
Refer to Appendix C “Properties of Rolled-Steel Sections” in the textbook.
The depth of the
The moment of inertia of the
Determine the moment of inertia (I) of the beam using the relation;
Here, the moment of inertia of the beam is
Refer to the cross section of the beam;
Substitute
Determine the distance from the neutral axis (c) to outer most fibre as follows;
Determine the width of the plates (b) using the relation.
Substitute
Therefore, the width of the plates is
Want to see more full solutions like this?
Chapter 5 Solutions
EBK MECHANICS OF MATERIALS
- How do i solve this problem?arrow_forwardQ4/ A compressor is driven motor by mean of a flat belt of thickness 10 mm and a width of 250 mm. The motor pulley is 300 mm diameter and run at 900 rpm and the compressor pulley is 1500 mm diameter. The shaft center distance is 1.5 m. The angle of contact of the smaller pulley is 220° and on the larger pulley is 270°. The coefficient of friction between the belt and the small pulley is 0.3, and between the belt and the large pulley is 0.25. The maximum allowable belt stress is 2 MPa and the belt density is 970 kg/m³. (a) What is the power capacity of the drive and (b) If the small pulley replaced by V-grooved pulley of diameter 300 mm, grooved angle of 34° and the coefficient of friction between belt and grooved pulley is 0.35. What will be the power capacity in this case, assuming that the diameter of the large pulley remain the same of 1500 mm.arrow_forwardYou are tasked with designing a power drive system to transmit power between a motor and a conveyor belt in a manufacturing facility as illustrated in figure. The design must ensure efficient power transmission, reliability, and safety. Given the following specifications and constraints, design drive system for this application: Specifications: Motor Power: The electric motor provides 10 kW of power at 1,500 RPM. Output Speed: The output shaft should rotate at 150 rpm. Design Decisions: Transmission ratio: Determine the necessary drive ratio for the system. Shaft Diameter: Design the shafts for both the motor and the conveyor end. Material Selection: Choose appropriate materials for the gears, shafts. Bearings: Select suitable rolling element bearings. Constraints: Space Limitation: The available space for the gear drive system is limited to a 1-meter-long section. Attribute 4 of CEP Depth of knowledge required Fundamentals-based, first principles analytical approach…arrow_forward
- - | العنوان In non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and v.-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: ti: final thickness V. Fig. (1) ofthrearrow_forwardA direct extrusion operation produces the cross section shown in Fig. (2) from an aluminum billet whose diameter 160 mm and length - 700 mm. Determine the length of the extruded section at the end of the operation if the die angle -14° 60 X Fig. (2) Note: all dimensions in mm.arrow_forwardFor hot rolling processes, show that the average strain rate can be given as: = (1+5)√RdIn(+1)arrow_forward
- : +0 usão العنوان on to A vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2R. Take: -9.81 mis ۲/۱ ostrararrow_forward: +0 العنوان use only In conventional drawing of a stainless steel wire, the original diameter D.-3mm, the area reduction at each die stand r-40%, and the proposed final diameter D.-0.5mm, how many die stands are required to complete this process. онarrow_forwardIn non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and vo-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: t₁: final thickness D₁ V. Fig. (1) Darrow_forward
- A vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2Rb. Take: 8-9.81 m/sarrow_forwardIn conventional drawing of a stainless steel wire, the original diameter D.-3mm, the area reduction at each die stand r-40%, and the proposed final diameter D₁-0.5mm, how many die stands are required to complete this process.arrow_forwardA vertical true centrifugal casting process is used to produce bushings that are 250 mm long and 200 mm in outside diameter. If the rotational speed during solidification is 500 rev/min, determine the inside radii at the top and bottom of the bushing if R-2Rb. Take: 8-9.81 m/sarrow_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