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 Z. Во 40mm |M 20mm
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- 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 MPaThe column shown is fabricated from two C250 x 30 standard steel shapes (see Appendix B for its cross-sectional properties) that are oriented back-to-back with a gap of 33 mm between the two channels. The column is fixed at its base and free to translate in the y direction at its upper end. Translation in the z direction, however, is restrained at its upper end. A load P is applied at an offset distance of 430 mm from the channel flanges. Use the AISC equations given in Section 16.5, and assume that L = 4.1 m, s = 33 mm, E = 200 GPa, oy = 275 MPa, and (Gallow); = 145 MPa. Offset - distance e P Lateral bracing in z direction C250 x 30 L C250 x 30 Cross section.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
- When sheer force acting on beam at F=60kN,find the sheer stress that occurs on the n-n section and indicate the distribution of the sheer stressThe Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7The 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.
- 1. Determine the moment M that should be applied to the beam in order to create a compressive stress at point D of op=30 MPa. Also sketch the stress distribution acting over the cross section and compute the maximum stress developed in the beam. A 25 mm M 150 mm `B - 25 mm 150 mm 25 mm 25 mmQ1/ A composite beam is made of wood and reinforced with steel strap located on its bottom side. It has the cross-sectional area shown in fig. if the beam is subjected to a bending moment of M=2kN.m, determine the normal stress at wood and steel. Take Ew=12Gpa and Est=200Gpa. 150mm Wood en 20mm Steel 150mmA 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 rod shown below is of diamater 70 mm and is fixed at one end. It is subjected to 500 N.m and 300 N.m torsional moments as shown. Sketch the distribution of the internal torsional moment along the length of the rod. Also find the torsional shear stress at points A and B, and also the largest shear stress in the rod. Point B is to the left of the 500 N.m torsional moment and A is on the right of it. Round-up your answers to the nearest 1/100th of an MPa. y 35 mm 20 mm 500 N.m 35 mm- 300 N.m Torsional shear stress at A = MPа %3D Torsional shear stress at B = MPа Maximum shear stress = MPa %3DFind 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.