The second moment of area of a rectangle is given by the formula I =bh^3/12 where b is the breadth and h is the height. Determine the approximate percentage error, if b is measured 3% too large and the height h is measured 1.7% too small. (Use the Binomial Expansion Method

The second moment of area of a rectangle is given by the formula I =bh^3/12 where b is the breadth and h is the height. Determine the approximate percentage error, if b is measured 3% too large and the height h is measured 1.7% too small. (Use the Binomial Expansion Method

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.16P: Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020...

See similar textbooks

Related questions

Q: 7.ON 5.0N 15 20 50 4.0N

A: To calculate the resultant force of the given system first determine the component of forces in x…

Q: Given is a thin-walled tube with the following data: Determine the following: a. Enclosed Area Wall…

Q: 100 Thus 1277 875 X <

A: Hi and thank you for the questions. Since you have asked multiple questions we will solve the first…

Q: Determine the magnitude of the reaction force at C in kN

A: Determine the magnitude of the reaction force at C

Q: 200 kN 40 kN/m z (m) 1 2.5

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the…

A: The force exerted on the dam by water pressure is 5.156 x 109 N.

Q: Calculate the change in dimensions in the bar. F = 12000 N; h= 0.01 m; w= 0.03 m;…

Q: A support beam has a length of 75 cm, width 35 cm and 50 cm thickness. What is the weight which the…

A: Given Data⇒ Length of beam(L)=75 cm=0.75 m Width(W)=35 cm=0.35 m Thickness(t)=50 cm=0.50 m…

Q: H.W.12 A cast iron pipe has an inside diameter of d = 208 mm and an outside diameter of D = 236 mm.…

A: Given data as per question Inside diameter of pipe =208 mm The outside diameter of the pipe =236 mm…

Q: How much deformation does a mass of 1 kg falling from a height of 6 meters cause to the built-in…

A: Given data:- mass, m=1kglength of beam, L=1.5m=1500mmwidth of beam, b=40mmdepth of beam, d=60mm⇒MOI…

Q: 4. The concrete seawall given in Figure 4 has a curved surface and restrains seawater at a depth of…

A: Given, Height of the seawater (H)=22.8m The density of the seawater=1030kg/m3 (assumed) Equation of…

Q: Example 10: Determine the resultant of the tensions of the wires shown in figure below. n' 12b 18tb…

A: Solution:

Q: Two branches of water pipe merge to form a larger diameter as shown figure below. At a location at…

Q: 220 40° 26° Find 225° d= 30 m R. d=40m

A: Given Datad1=40md2=50mγ=?α=? Here we are naming the triangle OAB and OPQ

Q: Solve for the hydrostatic force per meter length acting on the radial tainter as shown in the…

Q: 05: Find the magnitude, location and slope of the resultant of the non-concurrent coplanar force…

Q: The nodal coordinates and the nodal displacements for some plane stress elastic element is listed in…

Q: 1. Which of the following can be obtained from the Mohr's Circle a. Stiffness b. Damping coefficient…

A: Due to guideline of Bartleby we are allowed to answer only question post other question separatly .…

Q: Calculate the percentage increase in length of a wire of diamter 2.5mm stretched by a force equal to…

Q: 3. Determine the most unfavorable arrangement of the crane loads and compute the maximum and minimum…

A: given data; ⇒reaction force at point A=RA⇒reaction force at point B=RB

Q: Question 4 4. A string has a diameter of 1 cm and the original length of 2 m. The string is pulled…

Q: b)A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area…

A: Given data:-Area MOI of cross-section about x-axis, Ix=11.5×106mm4depth of cross-section, d=180mmThe…

Q: Question One: Derive expressions for determining the change in length for the following bodies P. b.…

Q: The parabolic arch is often used in construction because of its great strength. The equation of the…

Q: Three pipes are connected in series. The first pipe has a diameter of 522 mm and a length of 644 m.…

Q: A supported beam is shown in the picture below. Determine the following items at point C 1. Internal…

A: The free-body diagram of the given beam can be drawn as below, Here, RAH is the horizontal reaction…

Q: Question 4: Two moments of equal magnitude are applied to the following circular cross-section, as…

A: COUPLE A physical quantity that gives rotation to the cross section area or A couple is a pair of…

Q: A 2 46 KN C 2 B 30 kN/m 1,5 D

Q: Q7: The S ft wall shown here stands 27 fn from the building. Find the length of the shortest…

A: Assume that the x is the distance along the ground surface rom one end of the beam to the wall…

Q: Q6: The following force of mortality is given: Hy = 0.02 + - for 0sys 100. 100-y' 200-y Find 10918:

A: It is given that, μy=0.02+1100-y+2200-y for 0≤y≤100 10q10 needs to be calculated in this problem.

Q: The ratio of change in volume to the original volume is known as O Young's Modulus Bulk modulus O…

Q: Three pipes are connected in series. The first pipe has a diameter of 542 mm and a length of 603 m.…

A: Given Diameter, D1 = 542 mm D2 = 434 mm D3 = 315 mm…

Q: Q7: The 8 ft wall shown here stands 27 ft from the building. Find the length of the shortest…

A: Consider the diagram shown below for the given system. Here,

Q: As a part of preliminary design study, the effects of wind loads on a 275 m high building are…

Q: For the area shown below defined by the two curves, to find ly by integration you use a dA element…

Q: Example: What is the pressure at the center of pipe B? B -y = 10 kN/m3 Y = 20 kN/m3 50 cm 10 cm 50…

A: Given, γ1=10 kN/m3γ2=20 kN/m3

Q: From the figure below, choose the correct answer of the following 6 kN 5 kN 3KN30° 13 0.2 m 4. A В…

A: Given: A beam is simply supported and point load acted at a different point.

Q: Use the graphical method to construct the shear-force diagram and identify the magnitude of the…

Q: 47. The value of 1 mm of Hg is equal to А. 1.333 N/m2 В. B. 13.33 N/m2 C. 133.3 N/m 2

A: Given pressure head in mm of Hg is

Q: 3.5 m 30° B Q0000

Q: 3. Calculate the percentage increase in length of a wire of diameter 2.5 mm stretched by a force…

A: As per given question Wire diameter =2.5mm Weight =100 kg Y =12.5×1010N/m2 we have to determine…

Q: 045. A horizontal Y is shown in figure. Determine the X and Y components of the force exerted in the…

Q: ii, If the length of each element is 5m and the k-EA/Lis given as shown, analyze the following…

Q: Example 14: An elastic rubber band is attached to points A and B as shown in Fig. Determine its…

Q: H.W.12 A cast iron pipe has an inside diameter of d = 208 mm and an outside diameter of D = 236 mm.…

Q: Cross section of a beam is as shown in Figure Q1(a),determine; (1i) center of gravity with respect…

A: Solution:

Q: Panous distributed forces are exerted on the beam shown, w(x) = 2.234 N/m, p(x) = 1.551 N/m, q(x) =…

Q: 2) USE THE METHOD OF SECTIONS TO FIND THE MAGNITUDE AND DIRECTION OF THE FORCE IN BAR CD SHOWN BELOW…

Question

The second moment of area of a rectangle is given by the formula I =bh^3/12
where b is the breadth and h is the height.
Determine the approximate percentage error, if b is measured 3% too large
and the height h is measured 1.7% too small.
(Use the Binomial Expansion Method)

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

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

Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020 (channel with a nominal depth of 10 in., weighing 201b/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following properties for the cross section: A=5.88in.2,Ix=78.9in.4, and Iy=2.81in.4. If two of these channels are welded together as shown in Fig. (b), find Ix and Iy for the resulting cross section.
a) A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous. b) The same rectangular cross-section beam in Q2b is subjected to a maximum bending moment of 25,000 Nm and experiences sagging. Assuming that the centroidal axis passes through the beam section at (d/2), calculate the maximum bending stress (σmax) the beam will experience. Give your answer in N/mm2 and to 2 decimal places.
a) A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous. b) The same rectangular cross-section beam in Q2b is subjected to a maximum bending moment of 25,000 Nm and experiences sagging. Assuming that the centroidal axis passes through the beam section at (d/2), calculate the maximum bending stress (?max) the beam will experience. Give your answer in N/mm2 and to 2 decimal places.
b)A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is 11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous c) The same rectangular cross-section beam in Q2b is subjected to a maximum bending moment of 25,000 Nm and experiences sagging. Assuming that the centroidal axis passes through the beam section at (d/2), calculate the maximum bending stress (?max) the beam will experience. Give your answer in N/mm2 and to 2 decimal places.
answer #2, then show your complete solution! Given: FN = 52 MN = 100 SN = 75
A conveyor 66 m long is inclined at an angle of 4 degrees to the horizontal and deposits material 8 m below its top end. Determine the distance the material is carried by this conveyor. Provide your answer in m and round to the nearest whole number.
The triangular plate is fixed at its base, and its apex A is given a horizontal displacement of 5 mm. Suppose that a= 640 mm
For a loaded cantilever beam of uniform cross section, the bending moment along the length is M(x) = 5x2 + 10x, where x is the distance in mm measured from the free end of the beam. What is the magnitude of shear force in the cross section at x = 10 mm.
Q: Shear of Thin-Walled Beams (open section 1. The figure below shows the cross section of a thin, singly symmetrical I-section. Show that the distance & of the shear center from the vertical web is given by d (1+12p) where p=d /h., The thickness is taken negligibly small in comparison with the other dimensions and fj < I,
The parabolic arch is often used in construction because of its great strength. The equation of the bridge arch in Fig. 538 is y=( 36/724)x^2-6.0x+181. Determine the dimensions (ft) B, C,D,and E if A=128.0 ft
An infinitely long cylindrical container has a cross section area of radius R, and is placed horizontally with gravity being in the −y direction, as shown in the figure. The cylinder is 50% filled with water (the shaded part), with density ρ. The other 50% of the volume in the cylinder is filled with air with constant pressure of p = p0. The length of the cylindrical container in the axial direction is W. c) Use control volume analysis and divergence theorem on the 4th quadrant water volume to compute the hydrostatic force acted on the 4th quadrant of the cylinder wall, as shown by the thickened line in the figure.
find the vertical displacement at Point B of the built-in entry in the figure by Castigliano's theorem. E=200 GPa I = 30.10^6 mm^4