A beam with a Z cross-section is subjected to a moment M, which has a magnitude of 20 kip in. The resisting moment Mr on the cross- section makes an angle a = 36.87° with the =- axis. The moments of inertia and product of inertia for the cross section are I = 8.83 in ¹, Iz = = 25.4 in and Iyz = 11.3 in. Determine the orientation of the neutral axis in degrees. Note: Write answer in 2 decimal places. M₂ 60.31 A 2 a in. y Centroid C 38 3 in. 6 in.

A beam with a Z cross-section is subjected to a moment M, which has a magnitude of 20 kip in. The resisting moment Mr on the cross- section makes an angle a = 36.87° with the =- axis. The moments of inertia and product of inertia for the cross section are I = 8.83 in ¹, Iz = = 25.4 in and Iyz = 11.3 in. Determine the orientation of the neutral axis in degrees. Note: Write answer in 2 decimal places. M₂ 60.31 A 2 a in. y Centroid C 38 3 in. 6 in.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

EXAMPLE 4.2 The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm²; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm?. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. %3D 0.4 m 0.3 m 30 kN D E -0.4 m 0.2 m
The system shown in the figure has a fixed support at A and an alumimum rod of 0.5m length at C. The beam AC is subjected to a point load of 20 kN at its midspan. In addition to that point load, alumimum rod is subjected to a temperature decrease of 25 °C. Determine the deflection and the rotation at point C. Anhunnd 70 GP in
B.2. Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: σ, X (M.1, M,1,)y+ (M, I. - M.1,-) z (1,1.-1²-) where My and M₂ are bending moments applied to a cross-section, and where ly, Iz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (i) What assumptions have been made in the derivation of the above expression? (ii) Indicate by means of a sketch the directions in which positive values of the bending moments My and M₂ act on a cut plane facing in the positive x direction.
(2) 1.250mm Rिgुचि bcam 600mm 300 mm 1,000mm Figure No. 4
Elementary beam theory predicts that the axial bending stress ox in a prismatic beam is given by: ox = (M.I,M,L)y+(M,I.-M.I.) (1,1₂-13/2) where My and M₂ are bending moments applied to a cross-section, and where ly, lz and lyz are second moments of area in the usual notation (Oxyz is a Cartesian coordinate system in which the x axis corresponds to the centroidal axis of the beam). (iii) A Z--section beam has the cross-section shown overleaf (see Figure QB2). The second moments of area of the section about the y and z axes are given as;; ly = 1.12x106mm² and I₂ = 2.87x106 mm4. Show that lyz = 1.35x106 mm² (use the parallel axis theorem). 100 60 10 y -10 10 60 Figure QB2 N (iv) Bending moments Mz = 2.0 kNm and My = 0 kNm act on a cross- -section of the beam of part (iii). Obtain an expression for the bending stress and sketch the orientation of the neutral axis with reference to the y and z axes. What is the maximum tensile value of the axial bending stress and where does it occur?
ASAP
Qt The forces Fi and F2 at on a beacket as shown in the Figure bekow. Deternine the magnitade of the rescitant force F- 100 N
Derive the equation of the resonance frequency of the uniform cantilever beam shown below by using method of conservation of energy. [Solution tips: Umax, maximum strain energy is equal to max. kinetic energy of vibrating body.] j'm dx ( M(x)² T. U = max El xp- 1/2
A simply supported beam of length L is subjected to a varying distributed load sin (3x/L) Nm-¹, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is
The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm^2; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm^2. For the 30 kN force shown, determine the deflection of B and E, respectively. 0.4 m 0.3 m B A 0.2 m OC -0.4 m 30 kN E
A rigid beam BC is suspended by rods AB and CD as shown in the figure. Rod AB is made in from aluminum while rod CD is made from steel. Determine the location/placement of the 75kN concentrated load within the beam BC such that the rigid beam BC will remain horizontal after deflection. Determine the axial deformation of rods AB and CD.
(a) Based on the theory of deflection beam, state the boundary conditions of two beamsas shown in Figure Q2(a).