A member having the dimensions shown is used to resist an nternal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as she b) about the y axis. Sketch the stress distribution for each case.

A member having the dimensions shown is used to resist an nternal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as she b) about the y axis. Sketch the stress distribution for each case.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.10.1P: Determine the shape factor f for a cross section in the shape of a double trapezoid having the...

See similar textbooks

Related questions

Q: The eye hook has the dimensions shown. If it supports a cable loading of 800 lb, determine the…

A: Draw the free-body diagram of the hook.

Q: The force P is applied at d = 50 mm from the bottom as shown. Compute the normal stress at section…

A: Given:P=84 KNd=50 mm

Q: 5 kN.m is applied to the purlin in a plane at an angle of 30 deg to the vertical y axis. If the…

A: givenM=5000Nm, θ=30οMx=5000×103 cos30ο=4.4×105 N-mmMy=5000×103sin 30ο=2.2×105 N-mm

Q: (b)With the aid of bending moment of diagram, determine the maximum tensile and compressieve…

Q: Q3) The circular shaft is supported by smooth journal bearings at A and B that only exert vertical…

Q: Area of each portion 5 m2. Find stress in portion AB

A: Given data : Force in portion AB=F Area of portion AB=A Required : Stress in portion AB

Q: am is subjected to a force of 1 S-section of the beam is 75cm the stress in the beam.

A: GIVEN:F=150KNA=75cm2

Q: Neutral axis is an axis passing .3 through the centroid of cross section. The bending moments Mx and…

A: The neutral axis is the axis that passes through the centroid of the given cross-section. As we…

Q: Q2/ For simple supported boam * Ine cross section al area is H. B The maximum bending equal to M…

Q: Determine the moment M that must be applied to the beam in order to create a maximum stress of 90…

A: Given Data Maximum stress to be created is : σ=90 MPa Now draw the cross-section of the beam

Q: The beam is made of steel that has an allowable stress of sallow = 24 ksi. Determine the largest…

A: (a) From given I-section, on using parallel axis theorem, moment of inertia about a z-z axis,…

Q: The hook is subjected to the force of 80 lb. Determine the state of stress at point B at section…

A: Given Diameter of the cross-section D=0.5 in. Force subjected on the hook F=80 lb.

Q: s) The aluminum machine part is subjected to a moment of M = 75 kN. Determine the maximum tensile…

Q: Prob 2. The cantilever beam below is made of steel (E200 GPa) and must support the distributed load…

Q: Question 1: A member having the dimensions shown is used to resist an internal bending moment of M…

A: ◆ The moment of inertia of the cross-section: Iz = 63.6162 × (10-6) , m4 Iy = 0.1112787 × (10-3) ,…

Q: The singular force F will be applied to the beam with a hollow rectangular cross section.…

Q: (c) Calculate the maximum compressive bending stress (Express the stress in Pa or MPa ) and…

Q: The couple M is applied to a beam of the cross section shown in a plane forming an angle β with the…

A: Given data Length of side AB, 80 mm. Length of side BD, 32 mm. Calculate the moment of inertia…

Q: For the surface area shown below, determine the second moment of area, the location of the neutral…

Q: 3. The beam has a rectangular cross section as shown. Check the strength of the beam if the…

A: The reaction at point B can be determined by taking moment about point A.

Q: A beam with the cross section as shown is subjected to a positive moment of 50 kip.in about the…

Q: M 300 N m 16mm mm C. 40 mm-- 40 mm

Q: Find the normal stress of members CB and BF of the truss shown. Cross sectional area of the members…

A: GIVEN DATA - A PLANE TRUSS GIVEN WE HAVE TO FIND STRESS IN MEMBER CB AND BF

Q: (i) The position of the horizontal neutral axis; The second moment of area of the section about the…

A: Consider the following diagram Consider the area and C.G of figure 1 from the bottom face Consider…

Q: (a) At section a-a, determine the magnitude of the shear stress in the beam at point H. (b) At…

A: for solution refer below images.

Q: Determine the moment M that will produce a maximum stress of 10 ksi on the cross section.

A: Given data σ=10 ksi

Q: Write down the stress components expression at point A (0x, oy, oz, 1 xy, T yz, T xz) Show the…

A: Stress in the x-axis is,σx=VxAWhere A is area of the cross-section,The shear stress due to torque…

Q: moment M that will produce a maximum stress of 60 12 mm -75 mm- -12 mm 12 mm B C 75 mm 250 mm D 12…

A: Given data: = Stress, σ=6 kN/mm2=6×103 N/mm2

Q: A steal structure is loaded as shown. Knowing that F-10 kN and L-1 m: di design the rod CD, if a-100…

Q: A member having the dimensions shown is used to resist an internal bending moment of 30Nm. Determine…

A: Given The width of the beam is w=200 mm. The depth of the beam is d=150 mm. The value of bending…

Q: The couple M is applied to a beam of the cross section shown in a plane forming an angle β with the…

A: Given:

Q: find the maximum shear stress assuming that F= 4500 N %3D

A: Given: F=4500 N To determine: Maximum shear stress

Q: The couple M is applied to a beam of the cross section shown in a plane forming an angle β with the…

A: It is given the I section, the couple at point C act on it of magnitude M=250 kip.inso the stress at…

Q: If M = 1 kip # ft, determine the resultant force the bending stresses produce on the top board A of…

A: The depth of centroid is y¯=d2y¯=1.5+12+1.52y¯=7.5 in Expression to calculate the moment of inertia…

Q: The couple M acts in a vertical plane and is applied to a beam oriented as shown. Determine (a) the…

A: Given data as per the question M=15 kip.in. Iz=21.4 in4Iy=6.74 in4

Q: runs through the beam so that no tensile stress is developed in the concrete at its center section…

A: Given: TO determine: Tensile stress developed in the concrete beam when normal stress is 0

Q: A beam has a rectangular cross-section and is subjected to the stress the distribution is shown in…

A: Given data b=6 inh=12 in

Q: Determine the resultant force the bending stress produces on the bottom Flange B (in kip). Express…

Q: Determine the stress at point A for the beam with the cross-section shown below. Show the…

Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

For the bending about z axis, c =
m
Mc
MPa
max
Iz
For the bending about y axis, c =
m
Mc
MPa
I
man z MPa
M.
KN-M
max r MPa.
M
kum
MPa
max r MPa
mar Z

A member having the dimensions shown is used to resist an internal bending moment of M kNm.
Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown)
(b) about the y axis. Sketch the stress distribution for each case.
Take:
M=
90
kNm
A mm
A=
200
mm
B=
150
mm
B mm
Solution:
The moment of inertia of the cross-section about z and y axes are
I;-4
1
- AB³
12
(10) m*
I
BA =
(10) m*

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

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

Question 1: A member having the dimensions shown is used to resist an internal bending moment of M kNm. Determine the maximum stress in the member if the moment is applied (a) about the z axis (as shown) (b) about the y axis. Sketch the stress distribution for each case. Take: M= 98 kNm mm A= 208 mm B= 158 mm B mm Solution: The moment of inertia of the cross-section about z and y axes are 1 AB³ 12 |(10-) m* 1 ВАЗ — 12 I, |(10) m* = For the bending about z axis, c = m Mc O pax MPа Iz For the bending about y axis, c = m Mc MPа Iy max z MPa KN=M Omax Y MPa. M KN-M MPa O max Z Omax Y MPa
Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10 kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section. From the figure Z 1 in 112 in y in → ← ¹ in 12 in D C B A ++ in The area is determined to be 2.0625 in². The distances from the neutral axis to the top and bottom surfaces are determined to be 0.858 x in and The second moment of area is determined to be 0.447 in 4. 1.017 xin.
Find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and bottom surfaces. Consider that the section is transmitting a positive bending moment about the z axis, Mz, where M₂ = 10 kip-in if the dimensions of the section are given in ips units, or M₂ = 1.13 kN·m if the dimensions are in Sl units. Determine the resulting stresses at the top and bottom surfaces and at every abrupt change in the cross section. From the figure, с - 12.5 B A y I 50 100 75 12.5- 12.5 25 D 100 The area is determined to be 3750 mm² The distances from the neutral axis to the top and bottom surfaces are determined to be 57.292 The second moment of area is determined to be 4.293 x 106 mm4. mm and 42.708 ✪ mm.
If the I-flange beam is subjected to a shear force V = 20 kN, calculate the transverse shear stress at the point A (considered located on the web part). The area moment of inertia of that section about its neutral axis N.A. is INA = 44.167 x (106) m4. Flange Web Select one: O 41 MPa 10 Mpa O 4.95 MPa O O 50 MPa 100 MPa 20 mm 100 mm A 100 mm 25 mm 150 mm 25 mm
Determine the moment M that must be applied to the beam in order to create amaximum stress of 90 MPa. Also sketch the stress distribution acting over the cross section.
A moment about the z-axis of 192 N-m is applied to a beam with dimensions b = 85 mm and h = 302 mm. If there are no other loads applied to the beam (My, P, Vy and Vz = 0), what is the normal stress at point F? Give your answer in kPa to two decimal places with negative indicating compression and positive indicating tension. b/4 М, h E Ihis F h/3 В M. D b/4
The beam shown is subjected to compressive force of C1/2 kN.m, and bending moment of C2 N.m, calculate the total stresses on both points A and B* Sigma A = Sigma B = C2=140 C1=90 Во 40mm 20mm
The aluminium machine part shown below is subjected to a moment of M = 75 N.m. Determine the bending stress created at points B and A on the cross section. Sketch the results on a volume element located at each of these points. A- 50mm 50mm 100mm 100mm 20mm B- M=8kN-m 20mm
The simply supported joist is used in the construction of a floor for a building. In order to keep the floor low with respect to the sill beams C and D, the ends of the joists are notched as shown. If the allowable shear stress is tallow = 350 psi and the allowable bending stress is sallow = 1500 psi, determine the height h that will cause the beam to reach both allowable stresses at the same time. Also, what load P causes this to happen? Neglect the stressconcentration at the notch.
If the internal moment acting on the cross-section is 800 N.m, determine the maximum tensile and compressive bending stresses acting in the beam. Sketch the stress-distribution acting on the cross-section.
The 40-mm diameter solid shaft ACBD is supported by two bearings at A and B. Due to the transmission of power to and from the shaft, the belts of the pulleys are subjected to the tension forces shown in the figure below. 1-Draw the moment and shear diagrams on the y z and y x planes 2-Determine the location and magnitude of the maximum bending (normal) stress. Hint draw the shaft cross section at that location and think of the associated stresses. 0.050 m 300 N 0.250 m 200 N 550 N 0.250 m 400 N 150m D 0.075 m
A beam section has the z-axis and y-axis as the principal centroidal axes and I₂ = 15 x 106 mm and I, = 8 x 10 mm. The beam carries a moment with components M₂ = 5 kN.m and M₁ = -4 kN.m. What is the stress at the location z = 35 mm and y = 60 mm within the beam section? Show your work Select one: a. -2.5 MPa b. 2.5 MPa c. Od. 37.5 MPa -37.5 MPa