ENGINEERING FUNDAMENTALS
6th Edition
ISBN: 9781337705011
Author: MOAVENI
Publisher: CENGAGE L
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Chapter 15, Problem 11P
To determine
Using MATLAB, plot the deflection of a beam and find the maximum deflection of the beam.
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(Figure 1)
Figure
30 mm
140 mm,
30 mm
30 mm
70 mm
30 mm
170 mm
1 of 1
Part A
Determine the distance to the centroid C of the beam's cross-sectional area.
Express your answer to three significant figures and include the appropriate units.
X =
Submit
Part B
Īy =
Value
μA
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< Return to
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Compute the moment of inertia Iy about the y' axis.
Express your answer to three significant figures and include the appropriate units.
Value
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ignment
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6.21 A cantilever beam shown in the accompanying
figure is used to support a load acting on a
balcony. The deflection of the centerline of
the beam is given by the equation:
- wx?
y=
-(x² – 4 Lx + 6L²)
24 EI
where
y = deflection at a given x location, (m)
w = distributed load
E = modulus of elasticity (N/m²)
I = second moment of area (m²)
x = distance from the support as shown (m)
L = length of the beam (m)
What is the appropriate unit for w if the
preceding equation is to be homogeneous in
units? Show all steps of your work.
Problem 6.21 A cantilever beam.
QUESTION 3
The beam in Figure 3 is roller supported at A and B, pinned at D and hinged at c. The location
of the hinge is given in the figure, where a is the last two digits of your matrix number (Example:
for matrix number 201234, a/100 = 0.34; for matrix number 201204, a/100 = 0.04). Given E as
200 GPa, and I as 11250 cm*.
a) Draw the deflected shape of the beam.
b) Using conjugate beam method, determine the deflection at point C. Indicate the direction
of the deflection.
100 kN
C
2 m
3 m
a/100*L
L = 6 m
Figure 3
Chapter 15 Solutions
ENGINEERING FUNDAMENTALS
Ch. 15.1 - Prob. 1BYGCh. 15.1 - Prob. 2BYGCh. 15.1 - Prob. 3BYGCh. 15.1 - Prob. 4BYGCh. 15.1 - Prob. 5BYGCh. 15.2 - Prob. 1BYGCh. 15.2 - Prob. 2BYGCh. 15.2 - Prob. 3BYGCh. 15.2 - What is an M-file?Ch. 15.5 - Prob. 1BYG
Ch. 15.5 - Prob. 2BYGCh. 15.5 - Prob. 3BYGCh. 15.5 - Prob. 4BYGCh. 15.5 - Prob. 5BYGCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12PCh. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - Prob. 20PCh. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - Prob. 27PCh. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - Prob. 30PCh. 15 - Prob. 31PCh. 15 - The Body Mass Index (BMI) is a way of determining...Ch. 15 - Prob. 33PCh. 15 - Prob. 34PCh. 15 - Prob. 35PCh. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Prob. 39PCh. 15 - Prob. 40P
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- Case 1: Uniform beam under distributed load. In the shown Figure, a uniform beam subject to a linearly increasing distributed load. The deflection y (m) can be expressed by W. (-x5 + 2L²x³ –- L*x) 120EIL y = Wo Where E is the modulus of elasticity and I is the moment beam Use the following parameters L-600 cm, E=50,000 kN/cm?, l= 30.000 cm“, w.=2.5 kN/cm, to find the requirements ertia (m*), L length (a) (r = L, y = 0) (r = 0, y = 0) (b) Plot the following quantities versus distance along the beam Moment M(x) = Eld²y/dx². Shear V(x) = Eld³y/dx³. Loading w(x) = –Eld*y/dx+.arrow_forwardSuppose we have a uniform beam that is 3.73 metres long has a flexural rigidity of 34301Nm. Find the deflection of the beam in millimetres if the beam is under a uniform load of 86N/m and is supported with simple supports at both ends. Fill out the table below with your answers. x�-coordinate Deflection (mm��) x=0.22 y(x)= x=1.38 y(x) = x=2.05 y(x) = x=2.98 y(x) = x=3.58 y(x) = Enter as many decimal places as your calculator allows (8 to 10). Your answer must be within ±0.0005±0.0005 of the correct answer to be considered correct.arrow_forward9. If a load of 60 kN is applied to a rigid bar suspended by 3 wires as shown in the above figure what force will be resisted by each wire? The outside wires are of Al, cross- sectional area 300 mm² and length 4 m. The central wire is steel with area 200 mm² and length 8 m Initially there is no slack in the wires E= 2x105 N/mm² for Steel = 0.667x105 N/mm2 for Aluminum 60 kN Alum, wires Steel wirearrow_forward
- The simply supported beam carries three concentrated loads as shown in the figure. Determine the beam deflection at a section 5.74 feet from the pin support if P = 3327lb, Q =5726lb, R = 7383|lb, E = 27348 , and I= 471. Round off your answer to 6 decimal places. y P Q ... + 3 ft+ 3 ft→ 3 ft→+ 3 ft→| Add your answerarrow_forwardConsider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degrees) is (Give answer up to three decimal places) All dimensions 10 Nm in mm $20 500 B 44 S $10 500 Carrow_forwardSuppose we have a uniform beam that is 3.40metres long has a flexural rigidity of 31915N Find the deflection of the beam in millimetres if the beam is under a uniform load of 24Nmand is supported with simple supports at both ends. Fill out the table below with your answers. x�-coordinate Deflection (mm��) x=0.14 y(x)�(�) = x=1.12 y(x)�(�) = x=1.80 y(x)�(�) = x=2.65 y(x)�(�) = x=3.06 y(x)�(�) = Enter as many decimal places as your calculator allows (8 to 10). Your answer must be within ±0.0005±0.0005 of the correct answer to be considered correct.arrow_forward
- Question 3: Open Ended The beam in the following diagram has the following numerical values in stiffness: 77 Stiffness in bending = 1 Stiffness in axial tension = 1 What would the new values of stiffness in bending and axial tension be if the Height of beam is doubled while the Width remains constant? What would the new values of stiffness in bending and axial tension be if the Width of beam is doubled while the Height remains constant?arrow_forward1. The figure below shows a roof canopy beam which is supported by a φ20 mm hanger rod. The roof beam is a W200×19 steel beam with a cross-sectional area A = 2480 mm2, section modulus, Sx = 163×103 mm3 and a moment of inertia Ix = 16.6×106 mm4. The modulus of elasticity for steel is 200 000 MPa. 1) Determine the beam reactions at A and B. 2) Determine the axial stress in the 20 mm hanger rod and in the W200x19 beam. 3) Determine the shear force and bending moment at the midspan of the beam 4) Determine the bending stress in the beam at the mid-span of the beam.arrow_forwardConsider a beam shown in the figure below. (Figure 1) Figure 1 ▼ of 1 400 lb/ft 6 ft 900 lb Part A Express the internal shear in terms of a for 0≤x≤6 ft, where x is in ft. Express your answer in terms of z. Express your answer using three significant figures. V= Submit V= V ΑΣΦ | Η Submit vec My Answers Give Up [VD ΑΣΦ | 41 Part B Express the internal shear in terms of x for 6 ft << 9 ft, where is in ft. Express your answer in terms of z. Express your answer using three significant figures. vec ? My Answers Give Up lb ? lbarrow_forward
- Consider a beam shown in the figure below. (Figure 1) Figure 1 ▾of 1 400 lb/ft 6 ft 900 lb Part A Express the internal shear in terms of x for 0≤x≤6 ft, where is in ft. Express your answer in terms of z. Express your answer using three significant figures. V= Submit V= ΑΣΦΗ ΤΗ Submit vec My Answers Give Up [VD ΑΣΦ | 4 Part B Express the internal shear in terms of z for 6 ft << 9 ft, where is in ft. Express your answer in terms of z. Express your answer using three significant figures. vec ? My Answers Give Up lb ? lbarrow_forwardThe figure shows the infinitely rigid bar (ACD) suspended by three steel wires of diameter d and elasticity E σy, whose maximum allowable stress in the elastic range is σy. On the bar, weighing W, it also exerts a point force P as indicated in the figure. W= 10 [kN], P=5 [kN], d=5 [mm], L=1 [m], b=50 [cm], E=190 [GPa] , σy= 200 [MPa]. a) Calculate the vertical reactions on each of the wires.If applicable, indicate what wires are at risk of collapse b) Calculate the deformations of each wire for the case shown in a) c) Calculate the maximum deformations in each wire so that their behavior remains in the elastic rangearrow_forwardThe beam shown in the figure is supported at roller A and pinned at B and has a uniformly distributed loading w = 34 kN/m over 1.5 m from the left-hand end and moment loading M = 33 kNm at 1.5 m from end B. Determine the bending moment at a section from the left-hand end of the beam X = 1.9 m. Input your answer as a value only in kNm to one decimal place and without +/- sign. w kN/m M kNm B X -1.5 m- -1.5 m- -1.5 m-arrow_forward
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