**Problem Description:**Consider the beam and loading shown. Knowing that \( d = 1.37 \) in. and \( E = 29 \times 10^6 \) psi, determine the magnitude and location of the largest downward deflection. (Round the final answers to three decimal places.)**Beam and Load Diagram:**- The beam \( ABCD \) is horizontally aligned with supports at \( A \) and \( D \).- There is a distributed load of \( 10 \) lb/in. acting downward across section \( BC \).- A concentrated point load of \( 200 \) lb is acting downward at point \( B \).- Lengths along the beam: - \( AB = 24 \) in. - \( BC = 16 \) in. - \( CD = 8 \) in. - Total length \( AD = 48 \) in.**Task:**Determine:1. The location \( x_m \) of the largest downward deflection (inches).2. The magnitude of the largest downward deflection (inches).**Input Fields:**- The location of the largest downward deflection is \( x_m = \_\_\_\_.\) in.- The magnitude of the largest downward deflection is \_\_\_\_ in. ↓

Draw the free-body diagram of the beam. Apply force equilibrium in horizontal direction. HD=0 Apply moment equilibrium about point A. 101632+20040-VD48=0VD=273.33 lb Apply force equilibrium in vertical direction. VA+VD=1016+200VA+273.33=360VA=86.67 lb Write the expression of moment about x-x axis. Mx=VAx-10x-2424+x-242=86.67x-5x-24x+24Mx=86.67x-5x2+2880 Write the expression for deflection. EId2ydx2=Mx=86.67x-5x2+2880EIdydx=43.335x2-1.667x3+2880x+C1EIy=14.445x3-0.41675x4+1440x2+C1x+C2 Apply boundary conditions. At x=0, y=0 then,0=14.44503-0.4167504+144002+C10+C2C2=0And, at x=48 in, y=0 then,0=14.445483-0.41675484+1440482+C148+0C1=-56312.064then,EIy=14.445x3-0.41675x4+1440x2-56312.064x Calculate the location of largest downward deflection. EIdydx=14.445x3-0.41675x4+1440x2-56312.064=0-0.41675x4+14.445x3+1440x2-56312.064=0xm=6.10 in Therefore, the location of largest downward deflection is 6.10 inches from left end. Calculate the magnitude of largest downward deflection. At x=6.10EIy=14.445x3-0.41675x4+1440x2-56312.064x29×106π64×1.374ymax=14.4456.103-0.416756.104+14406.102-56312.0646.10ymax=-0.0573 in|ymax|=0.0573 in Therefore, the magnitude of largest downward deflection is 0.0573 inches.

Engineering

Mechanical Engineering

Consider the beam and loading shown. Knowing that d=1.37 in. and E= 29 x 106 psi, determine the magnitude and location of the largest downward deflection. (Round the final answers to three decimal places.) 24 in. B 10 lb/in. 16 in. 48 in. 200 lb D -8 in. d The location of the largest downward deflection is Xm³ The magnitude of the largest downward deflection is in. in. I.

Consider the beam and loading shown. Knowing that d=1.37 in. and E= 29 x 106 psi, determine the magnitude and location of the largest downward deflection. (Round the final answers to three decimal places.) 24 in. B 10 lb/in. 16 in. 48 in. 200 lb D -8 in. d The location of the largest downward deflection is Xm³ The magnitude of the largest downward deflection is in. in. I.

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

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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

**Problem Description:**
Consider the beam and loading shown. Knowing that \( d = 1.37 \) in. and \( E = 29 \times 10^6 \) psi, determine the magnitude and location of the largest downward deflection. (Round the final answers to three decimal places.)

**Beam and Load Diagram:**

- The beam \( ABCD \) is horizontally aligned with supports at \( A \) and \( D \).
- There is a distributed load of \( 10 \) lb/in. acting downward across section \( BC \).
- A concentrated point load of \( 200 \) lb is acting downward at point \( B \).
- Lengths along the beam:
- \( AB = 24 \) in.
- \( BC = 16 \) in.
- \( CD = 8 \) in.
- Total length \( AD = 48 \) in.

**Task:**
Determine:
1. The location \( x_m \) of the largest downward deflection (inches).
2. The magnitude of the largest downward deflection (inches).

**Input Fields:**
- The location of the largest downward deflection is \( x_m = \_\_\_\_.\) in.
- The magnitude of the largest downward deflection is \_\_\_\_ in. ↓

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