ENGINEERING FUNDAMENTALS
6th Edition
ISBN: 9781337705011
Author: MOAVENI
Publisher: CENGAGE L
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Chapter 6, Problem 21P
To determine
Calculate the appropriate unit for the distributed load
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Consider the T-beam shown in (Figure 1). Suppose that
a = 80 mm, b=160 mm, c = 10 mm.
Figure
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1 of 1
Determine y, which locates the centroidal axis x' for the cross-sectional area of the T-beam.
Express your answer to three significant figures and include the appropriate units.
y =
Submit
Part B
IT' =
Submit
Part C
Value
Determine the moment of inertia I.
Express your answer to three significant figures and include the appropriate units.
Request Answer
Iy' =
Value
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Units
Value
Units
?
Determine the moment of inertia Iy'.
Express your answer to three significant figures and include the appropriate units.
Units
?
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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.
Suppose 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.
Chapter 6 Solutions
ENGINEERING FUNDAMENTALS
Ch. 6.1 - Prob. 1BYGCh. 6.1 - Prob. 2BYGCh. 6.1 - Prob. 3BYGCh. 6.1 - Prob. 4BYGCh. 6.1 - Prob. BYGVCh. 6.2 - Prob. 1BYGCh. 6.2 - Prob. 2BYGCh. 6.2 - Prob. 3BYGCh. 6.2 - Prob. 4BYGCh. 6.2 - Prob. 5BYG
Ch. 6.2 - Prob. 6BYGCh. 6.2 - Prob. BYGVCh. 6.3 - Prob. 1BYGCh. 6.3 - Prob. 2BYGCh. 6.3 - Prob. 3BYGCh. 6.3 - Prob. 4BYGCh. 6.3 - Prob. BYGVCh. 6.5 - Prob. 1BYGCh. 6.5 - Prob. 2BYGCh. 6.5 - Prob. 3BYGCh. 6.5 - Prob. 4BYGCh. 6.5 - Prob. BYGVCh. 6.6 - Prob. 1BYGCh. 6.6 - Prob. 2BYGCh. 6.6 - Prob. 3BYGCh. 6.6 - Prob. BYGVCh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10PCh. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - The air resistance to the motion of a vehicle is...Ch. 6 - Prob. 25PCh. 6 - Prob. 26PCh. 6 - Prob. 27PCh. 6 - Prob. 28PCh. 6 - Prob. 29PCh. 6 - Prob. 30PCh. 6 - Prob. 31PCh. 6 - Prob. 32PCh. 6 - Prob. 33PCh. 6 - The calorie is defined as the amount of heat...Ch. 6 - Prob. 35PCh. 6 - Prob. 36PCh. 6 - Prob. 37PCh. 6 - Prob. 38PCh. 6 - Prob. 39PCh. 6 - Prob. 40PCh. 6 - For the fin equation described in Problem 6.25, if...Ch. 6 - Prob. 42PCh. 6 - Prob. 43PCh. 6 - Prob. 44PCh. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - Prob. 47PCh. 6 - Prob. 48PCh. 6 - Prob. 49PCh. 6 - Prob. 50PCh. 6 - Prob. 51P
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- Consider the beam shown in (Figure 1). Suppose that a = 160 mm, b=210 mm, c= 50 mm. Figure 1 of 1 a a Part A Determine the moment of inertia of the beam's cross-sectional area about the centroidal z axe. Express your answer to three significant figures and include the appropriate units. I₂ = Submit Part B Iy= μA Submit Value Determine the moment of inertia of the beam's cross-sectional area about the centroidal y axe. Express your answer to three significant figures and include the appropriate units. Units My Answers Give Up μA Value Units ? My Answers Give Up ? Provide Feedback Continuearrow_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_forwardQUESTION 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 3arrow_forward
- Part D - Analyzing a system of forces acting on a concrete slab The concrete slab shown in the picture is subject to four forces, F1=125 lb, F2=260 lb, F3=675 lb, and F4=255 lb. (Figure 3) The dimensions are d1=8.0 ft, d2=24 ft, d3=3.0 ft, d4=13 ft, and d5=9.5 ft. Determine the equivalent resultant force by specifying its magnitude and its location (x,y) on the slab. Express your answers, separated by commas, to three significant figures. FR, x, y= lb, ft,ftarrow_forwardThe 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_forward1. The following equation describes the relationship between the maximum deflection of the end of a beam and the applied load. PL3 = 3EI a) If ð is the maximum deflection in inches, L is the length of the beam in inches, P is the load in pounds, and E is the Young's Modulus in pounds/in?, find the units for I (moment of inertia). b) The measured deflection for a specific beam under loading is measured to be .01 in. Convert this to millimeters.arrow_forward
- Consider 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_forwardQuestions QI. Calculate the bending stresses at top and bottom fibers of a simply supported beam and loaded as shown in figure below. The cross section of the beam is an I-section as shown. 250 38 2 kN X kN 300 25 5 kN/m 38 D. 1.5 m 150 2.2 m 2 m All dimensions are in mm Take X= Last digit of your student id and if the last digit is zero, then take X 2.5 kN.arrow_forwardA 20-cm-diameter steel rod is subjected to a tensile load of 1000KN at one end and is fixed at the other end. Calculate the deflection of the rod if it is 150-cm long. (Esteel 200 GPa) PL d = AE where d= end deflection of the bar in meter (m) P= applied load in newton (N) %3D L = length of the bar in meter (m) %3D A = cross-sectional area of the bar in m E = modulus of elasticity of the material (N/m) O 0.73 mm 0.1.51 mm 0.02 mm 0.24 mmarrow_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_forwardCase 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_forwardFor the beam cross section shown below, an applied anticlockwise torque of 30,000 Nmm is applied, but no other forces. d b By doing an equal twist analysis, we know that q1 = 2.5 x qi1 The dimensions are: a = 121 mm b=277 mm c= 117 mm d=71 mm Calculate the value of q11 Enter your answer as N/mm, to 3 significant figures, but without the units. You have an error margin of 3%. Type your answer.arrow_forward
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