(a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm2, I= 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (1) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b)

(a) A steel beam in the form of a cantilever of length 2 m, designed for a structural engineering application, is required to carry a load of 40 kN at the free end as shown in Figure 4(a). As the engineer implementing the design, you want to make a reasonable estimate of the vertical deflection at the free end. Using the double integration approach, calculate the end deflection. E = 200 GNm2, I= 15 x 10 mª. (b) As the end deflection is of unacceptable magnitude for the intended purpose, the design team suggests that the cantilever be simply supported at the middle of its length to the level of the fixed end as shown in Figure 4(b). (1) (ii) (iii) What is the main difference between the two problems from a structural analysis standpoint? To re-calculate the end deflection and the load R on the prop, using Macaulay's method, write the expression for bending moment in the entire beam and then integrate the moment equation for slope and deflection. State the boundary conditions which will lead to determination of the constants in the above expressions; the constants need not be calculated. 40 KN 2m Figure 4(a) 40 KN 1m 1m R Figure 4(b)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: For the configuration shown in Figure P6.11, determine the deflection at the point of load…

A: Given:To find:Deflection at the point of load application.

Q: Parvinbhai

A: The objective of this question is to determine the deflection at the free end of a cantilever beam…

Q: 2. Consider the following steel shaft (E = 30 x 106 psi) A w-200 lb/in 0.75d 0.75d V 5 in.- 15 in. A…

A: To findWhat is the diameter d so the deflection at the middle is not larger than 0.2 mmgivenModulus…

Q: BP2: A simply supported beam length of 2 m is redundantly supported at 1/3=0.67 m and carries a…

A: The given is as shown below,

Q: For the cantilever steel beam [E = 190 GPa; I = 145 × 106 mm*], use the double-integration method to…

Q: The simply supported beam consists of a W21 x 44 structural steel wide-flange shape [E = 29,000 ksi;…

A: (a) Draw the free-body diagram of the given beam. Apply force equilibrium in horizontal direction.…

Q: ed to a point load of 10kN, and is supported at both ends by fixed connections. Calculate the eam,…

Q: 1. In a close coiled spring there are 27 coils of solid round wire 3mm in diameter,the mean diameter…

A: According to the given data d=3 mm D=30mm n=27 G=93 KN/mm2 P=50 N We need to find The deflection in…

Q: the deflection of a beam whose length is 6 m with the modulus of elasticity of E = 200 GPa and I =…

A: Given data: E = 200 GPa = 200×109 N/m2 I = 98×106 mm4 = 98×10-6 m4 distributed load, w = 13000 N/m…

Q: A circular plate with simply supported edges subjected to a uniform pressure of P=440 KPa, as shown…

A: The maximum deflection of a beam can be minimized by utilizing harder materials, increasing the…

Q: 1. Consider the following steel shaft (E = 30 × 106 psi) 0.75d 5 in.-4 w = 200 lb/in. 15 in. 0.75d 5…

A: The elasticity of the beam is E=30*106 psi. The deflection of the center is not more than 0.2 mm.

Q: ONLY SOLVE PART B Find the deflection y(x) differential equations where: a)The beam is embedded at…

A: Draw the beam showing the load as given below. Here W signifies load. Determine the sheer force for…

Q: Need help with parts a-e

A: Step 1:Step 2:Step 3:Step 4:

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

4.
(a)
A steel beam in the form of a cantilever of length 2 m, designed for a
structural engineering application, is required to carry a load of 40 kN at
the free end as shown in Figure 4(a).
As the engineer implementing the design, you want to make a
reasonable estimate of the vertical deflection at the free end. Using
the double integration approach, calculate the end deflection. E = 200
GNm², I = 15 x 10 mª.
(b)
As the end deflection is of unacceptable magnitude for the intended
purpose, the design team suggests that the cantilever be simply
supported at the middle of its length to the level of the fixed end as
shown in Figure 4(b).
(i)
(ii)
(iii)
What is the main difference between the two problems from
a structural analysis standpoint?
To re-calculate the end deflection and the load R on the prop,
using Macaulay's method, write the expression for bending
moment in the entire beam and then integrate the moment
equation for slope and deflection.
State the boundary conditions which will lead to determination of
the constants in the above expressions; the constants need not
be calculated.
40 KN
2m
Figure 4(a)
40 KN
1m
1m
R
Figure 4(b)
401

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Determine the net deflection at the free end using double integration method.

VIEW

Step 2: The net deflection at the free end.

VIEW

Step 3: Determine the net deflection at the free end using Macaulay's method.

VIEW

Step 4: Solved the modified system using Macaulay's method.

VIEW

Solution

VIEW

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

A long, slender structural aluminum [E = 69 GPa] flanged shape is used as a L = 9.2-m-long column. The column is supported in the x direction at base A and pinned at ends A and C against translation in the y and z directions. Lateral support is provided to the column so that deflection in the x-z plane is restrained at mid-height B; however, the column is free to deflect in the x-y plane at B. Assume that b; = 102 mm, d = 122 mm, t; = 8 mm, and tw = 6 mm. Determine the maximum compressive load P the column can support if a factor of safety of 2.9 is required. In your analysis, consider the possibility that buckling could occur about either the strong axis (i.e., the z axis) or the weak axis (i.e., the y axis) of the aluminum column. P bf C d Lateral В bracing 2 Determine the moment of inertia with respect to the y and the z axes through the centroid of the cross section area. Answers: ly = i mm“, Iz = i mm4.
h F The beam of length 5.9 (m) and cross section base 0.10 (m) and height 0.16 (m) shown is made of plain steel with a modulus of elasticity of 200 (Gpa) and an ultimate strength of 400 (Mpa). The load is 250 (N) and the point q is 4.0 (m) from the wall in the x direction. What is the magnitude of vertical deflection of the beam at point q in units of meters?
A bi-metallic cantilevered strip (i.e. horizontally composite beam) is to operate a switch at its free end. The steel and bronze strips are each 100 mm long and 15 mm x 1 mm in cross-section. Calculate the common radius of curvature and deflection at the free end for a temperature rise of 50 C. Take E = 200 GPa, a = 10 × 10-6 /C for steel and E = 120 GPa a = 20 x 106 /C for bronze.
For the cantilever steel beam [E = 230 GPa; 1= 86 x 106 mm4], use the double-integration method to determine the deflection vg at B. Assume L = 3.3 m, Mo = 79 kN-m, and w = 11 kN/m. "| A Answer: VB = i W L mm. B Mo
Shown below is a rigid beam ABC that is connected by pinned connections to rod (1) at A, rod (2) at C, and pivots freely at B. Rod (1) is made of bronze (E=100GPA, a=16.9x10-6/°C) and is 24mm in diameter. Rod (2) is made of aluminum (E=70GPA, a=22.5x10-6/°C) and is 16mm in diameter. The bars are unstressed as shown at 25°C. The temperature of bar (2) is reduced to 10°C while the temperature of bar (1) is held constant. Find the normal stress in bars (1) and (2). 250mm (1) |이 B A 200mm 350mm 500mm (2)