**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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