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
Mechanics Of Materials - Si Version
- Knowing that P=Q= 480 N, determine (a) the distance a for which the absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending.arrow_forwardEach of the three aluminum bars shown is to be twisted through an angle of 2.1°. Knowing that b = 30 mm, τall = 50 MPa, and G = 27 GPa, determine the shortest allowable length of each bar. Refer to Table 3.1. The shortest allowable length of bar (a) is mm. The shortest allowable length of bar (b) is mm. The shortest allowable length of bar (c) is mm.arrow_forwardFor the wide-flange beam with the loading shown, determine the largest load P that can be applied, knowing that the maximum normal stress is 160 MPa and the largest shearing stress is 100 MPa. W360 x 122 Barrow_forward
- A weightlifting bar is loaded symmetrically in A and D (P = 1500N of each side). The weightlifter's hands are located at B and C, 0.45 m from A and D. Determine the maximum bending moment in the bar ABCD and the minimum diameter d of the bar knowing that the constraint admissible for the material of the bar is 200MPa.arrow_forwardA 10-ft rope is attached to two supports A and b as shown. Determine (a) the span of the rope for which the span is equal to the sag, (b) the corresponding angle 0B.arrow_forwardFor the beam with the cross-section shown, given that: V= 100 N b= 20 cm h=20 cm The max shear stress equals:arrow_forward
- Knowing that the bending moment in the reinforced concrete beam is 1100 kip?ft and that the modulus of elasticity is 3.625 *106 psi for the concrete and 29* 106 psi for the steel, determine (a) the stress in the steel, (b) the maximum stress in the concretearrow_forwardThe 24-ft timber floor joist is designed to carry a uniformly distributed load. Because only 16-ft timbers are available, the joist is to be fabricated from two pieces connected by a nailed joint D. Determine the distance b for the most advantageous position of the joint D, knowing that nailed joints are strong in shear but weak in bending.arrow_forwardLink AB, of width b =50 mm and thickness t = 6 mm, is used to support the end of a horizontal beam. Knowing that the average normal stress in the link is 2140 MPa, and that the average shearing stress in each of the two pins is 80 MPa, determine (a) the diameter d of the pins, (b) the average bearing stress in the link.arrow_forward
- A fabric used in air-inflated structures is subjected to a biaxial loading that results in normal stresses ox = 18 ksi and oz = 24 ksi.Knowing that the properties of the fabric can be approximated as E = 12.6 x 10 psi and v = 0.34, determine the change in length of (a) side AB, (b) side BC, (c) diagonal AC.arrow_forwardHelp me i need solve this _II_ A steel plate 10 mm thick is embedded in a horizontal concrete slab and is used to anchor high strength vertical cable as shown. The diameter of the hole in the plate is 24 mm. the ultimate strength of the steel used is 250 MPa. and the ultimate bonding stress between plate and concrete is 2.1 MPa. Knowing that a factor of safety of 3.60 is desired when P = 18 kN. Determine: a) the required width a of the plate. b) the minimum depth bb to which a plate of that width should be embedded in the concrete slab. (Neglect the normal stresses between the concrete and the lower end of the plate.)arrow_forwardFor the beam and loading shown, determine the minimum required width b, knowing that for the grade of timber used, σall= 12 MPa and τall= 825 kPa.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L