Textbook: Strength of Materials Please provide step by step solution. A formula sheet is provided for your reference. The cross section of a beam is shown below. The formula for the Moment of Inertiaabout the x-axis at the centroid of the section is shown below.Outer Diameter = 50 mmInner Diameter = 40 mmIxc = (douter - dinner)dinmer)64a) Solve for the moment of inertia, about the x-axis at the centroid.b) Using the parallel axis theorem, solve for the moment of inertia, about the x-axis atthe top of the shape. Formula SheetCentre of Gravity and Moment of InertiaΣΑΣΑEA,ΣΑI, = I, + Ad² I¸ =E(!.)+ E(Ad²)1, = E(!.)+yAxial Stress and Internal ForcesΣΕ, -0 Σ , =0 ΣΜ=0o = P/ AT =V | AS.F. = o alow /o.allowactualStrainPL8 =AE· E \ateralV =E =E =LE axial

To determine the Moment of Inertia (MOI) of the given section about the x-axis at the centroid, we…

Answered: Solve for the moment of inertia, about…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The beam cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 470 mm tw = 14 mm d = 120 mm t = 9.6 mm Additionally: • The area of each pipe is A = 3330 mm2. • The moment of inertia of the entire beam cross section about the z centroidal axis is IZ = 428040000 mm4. If the beam will be subjected to a shear force of V = 225 kN, determine the shear stress at point H, located at yH = 110 mm above the z centroidal axis.
A non-prismatic cantilever beam of length L carries a vertical load P at its free end on the right. The section of the beam changes midway along its length so that the moment of inertia of its cross-section is reduced by half. The smaller section is towards the free end. If E is constant, determine the deflection at the free end. O P(L^3)/ (16EI) O 3P(L^3)/(6EI) O3P(L^3)/(16EI) O P(L^3)/(EI)
The bear cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 390 mm tw - 14 mm d = 100 mm t = 4.8 mm Additionally: • The area of each pipe is A = 1436 mm². • The moment of inertia of the entire bear cross section about the z centroidal axis is lz=140920000 mm². If the bearn will be subjected to a shear force of V = 170 kN, determine the shear stress at point H, located at y = 100 mm above the z centroidal axis.
The beam cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 430 mm tw = 16 mm d = 110 mm t= 6.4 mm Additionally: • The area of each pipe is A = 2083 mm². • The moment of inertia of the entire beam cross section about the z centroidal axis is lz=241870000 mm4. If the beam will be subjected to a shear force of V=235 kN, determine the shear stress at point K, located at yk = 70 mm below the z centroidal axis. H H K Answer: TK = z MPa Уи Yk
The beam cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 390 mm tw = 12 mm d = 100 mm t = 6.4 mm Additionally: • The area of each pipe is A = 1882 mm². • The moment of inertia of the entire beam cross section about the z centroidal axis is lz=171660000 mm4. If the beam will be subjected to a shear force of V = 120 kN, determine the shear stress at point H, located at yμ = 100 mm above the z centroidal axis. H Hv K Answer: TH= X MPa Ун Ук K Iv
The beam cross section shown below has been proposed for a short pedestrian bridge. The cross section will consist of two pipes that are welded to a rectangular web plate. Dimensions of the cross section are: h = 430 mm t₁ = 14mm d = 110 mm t = 9.6 mm Additionally: • The area of each pipe is A = 3028 mm². • The moment of inertia of the entire beam cross section about the z centroidal axis is lz= 325870000 mm². If the beam will be subjected to a shear force of V=245 kN, determine the shear stress at point H, located at y = 110 mm above the z centroidal axis. d H.V Answer: TH= x Z MPa Уи YK H K
Beam AB is made of three plates glued together and is subjected, in its plane of symmetry, to the loading shown. Knowing that the shear force is V=3.5kN and I=8.63*106 m“, determine the following: -100 mm 20 mm -Joint a 80 mm C 20 mm - 68.3 mm 20 mm 60 mm The value of Q is equal to in m3: The value of t for the Joint a is equal to in mm: The average shearing stress at Joint a is equal to in kPa:
A circular steel rod AB of diameter d1,length L and modulus of rigidity G is loaded as shown is figure. A rigid bar BC of length b is rigidly fixed to AB at B such that BC is perpendicular to AB and lies in the horizontal plane. Find the deflection of point C due to (i) Bending of AB (ii) Torsion of AB (iii) Combined bending and torsion L P B
For the beam shown in the figure determine the following: (EI = constant)a. value of EIθ at Ab. value of EIθ at Cc. value of EIδ at Bd. value of EIδ at D
There is a beam as shown in the figure below, and the flexural stiffness of the beam section is constant EI:(a) Try the Moment-area Method to obtain the slope of point A after deformation.(b) Same as the above question, try to find the slope of point B after deformation.(c) Same as the question above, try to find the vertical deflection of point C (Deflection).
Problem 2: Deflection Calculation Determine the maximum deflection of the beam loaded as shown in the figure below using Conjugate beam method. Also draw the deflected shape of the beam. El is uniform throughout the beam. A is a roller support, and C is fixed support. There is an internal hinge/pin at B. The value of P must be calculated using your student ID and the following equation P(kN) = [(V218503042) – C]/4 C=14700 So, P= 20 kN 4P 2P 3 m 6 m 2 m 2 m Find 1. BMD of real beam 2. Conjugate beam+ loading 3. Reactions of conjugate beam 4. Location of maximum deflection 5. Maximum deflection & its direction 6. Deflected shape of the beam
A beam is shown in the figure below, and the flexural stiffness of the beam section is constant EI:(a) Use the Moment-area Method to find the Slope after point A is deformed.(b) Same as above, try to find the slope of point B after deformation.(c) Same as above, try to find the vertical deflection of point C (Deflection).

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Solve for the moment of inertia, about the x-axis at the centroid. Using the parallel axis theorem, solve for the moment of inertia, about the x-axis at the top of the shape.