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Given: Maximum positive shear = 387.50 kN Maximum negative shear = 602.50 kN Maximum positive moment = 1970.65 kN-m Maximum negative moment = 1480 kN-m Location of maximum shear from the left end of beam = 22 m Location of maximum moment from the left end of beam = 15.23 m   Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure.  Note: Measurements in figure is in millimeters. Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.

Given: Maximum positive shear = 387.50 kN Maximum negative shear = 602.50 kN Maximum positive moment = 1970.65 kN-m Maximum negative moment = 1480 kN-m Location of maximum shear from the left end of beam = 22 m Location of maximum moment from the left end of beam = 15.23 m   Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure.  Note: Measurements in figure is in millimeters. Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.

Structural Analysis
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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Given:

Maximum positive shear = 387.50 kN

Maximum negative shear = 602.50 kN

Maximum positive moment = 1970.65 kN-m

Maximum negative moment = 1480 kN-m

Location of maximum shear from the left end of beam = 22 m

Location of maximum moment from the left end of beam = 15.23 m

 

Determine the maximum bending stress (in MEGAPASCALS on the beam) given the cross-section on figure. 

Note: Measurements in figure is in millimeters.

Kindly Draw the Shear and Moment Diagram or FBD if necessary. Compute for all of the necessary elements, Include the proper units, use the proper formula and round-off all the answers and final answers to 2 decimal places.

Mechanics of Deformable Bodies I = bh3 SHEAR STRESS FORMULA 12 Mc Mc or Bending Stress I I Area = A' MOVING LOADS For more than one moving Load: 1. The bending moment under a particular load is a maximum when the center of the beam is midway between that load and the resultant of all loads on the y' A span of the beam. 2. The maximum shear occurs at the reaction where the resultant load is nearest. Usually, it happens if the biggest load is over that support and as many as possible of the remaining loads are still on the span. PROCEDURE: 1. Determine the location of the Resultant relative to the given loads. 2. Put the center of the load and the resultant to coincide with the beam. 3. Calculate supports. 4. Section/cut the beam where the load in consideration is located. The shear stress in the %3D VQ T = It member at the point located at a distance This stress is assumed to be constant and therefore averaged y from the neutral axis. across the width t of the member. MOST ECONOMIC SECTIONS V= the shear force I = the moment of inertia of the ENTIRE cross- sectional area calculated about the neutral axis. When a structural section is selected to be used as a beam, the section modulus must be equal to or greater than the section modulus determined by the flexure equation; t = the width of the member's cross section measured at the point where the shear stress is to be determined. |M\max Oallow This equation indicates that the section modulus of the selected beam must be equal to or greater than the ratio of the bending moment to the working stress. A design engineer is often required to select the lightest standard structural shape (such as a W-shape) that can carry a given loading in addition to the weight of the beam. Following is an outline of the selection process: 1. Determine the maximum shear and moment of the (loaded) beam. A V-M diagram is the fastest way to do it. Neglect beam weight at this point. 2. Determine the minimum allowable section Q = 2ÿ'\A'j + y½A'½ modulus, Smin 3. Choose the lightest shape from the list of structural shapes where S> Smin 4. Calculate the maximum bending stress in the selected beam caused by the loading PLUS the beam self weight. If ơmax < Oallow then the selection is finished. If it is not satisfied, choose the second lightest shape. 5. Repeat the selection process until a satisfactory, economic shape is found. Q = j'A' Q = j'A' Q = j' A', where A' is the area of the top (or bottom) portion of the member's cross-section, above (or below) the section plane where t is measured and y' is the distance from the neutral axis to the centroid of A'. or A'= Area of the section above/below t. j' = Distance of the centroid of A' to Neutral Axis (N.A.) 4r E(А) (Location of Neutral Axis) = y = ΣΑ (I about the Neutral Axis) I = Iy'+ Ad,?
Transcribed Image Text:Mechanics of Deformable Bodies I = bh3 SHEAR STRESS FORMULA 12 Mc Mc or Bending Stress I I Area = A' MOVING LOADS For more than one moving Load: 1. The bending moment under a particular load is a maximum when the center of the beam is midway between that load and the resultant of all loads on the y' A span of the beam. 2. The maximum shear occurs at the reaction where the resultant load is nearest. Usually, it happens if the biggest load is over that support and as many as possible of the remaining loads are still on the span. PROCEDURE: 1. Determine the location of the Resultant relative to the given loads. 2. Put the center of the load and the resultant to coincide with the beam. 3. Calculate supports. 4. Section/cut the beam where the load in consideration is located. The shear stress in the %3D VQ T = It member at the point located at a distance This stress is assumed to be constant and therefore averaged y from the neutral axis. across the width t of the member. MOST ECONOMIC SECTIONS V= the shear force I = the moment of inertia of the ENTIRE cross- sectional area calculated about the neutral axis. When a structural section is selected to be used as a beam, the section modulus must be equal to or greater than the section modulus determined by the flexure equation; t = the width of the member's cross section measured at the point where the shear stress is to be determined. |M\max Oallow This equation indicates that the section modulus of the selected beam must be equal to or greater than the ratio of the bending moment to the working stress. A design engineer is often required to select the lightest standard structural shape (such as a W-shape) that can carry a given loading in addition to the weight of the beam. Following is an outline of the selection process: 1. Determine the maximum shear and moment of the (loaded) beam. A V-M diagram is the fastest way to do it. Neglect beam weight at this point. 2. Determine the minimum allowable section Q = 2ÿ'\A'j + y½A'½ modulus, Smin 3. Choose the lightest shape from the list of structural shapes where S> Smin 4. Calculate the maximum bending stress in the selected beam caused by the loading PLUS the beam self weight. If ơmax < Oallow then the selection is finished. If it is not satisfied, choose the second lightest shape. 5. Repeat the selection process until a satisfactory, economic shape is found. Q = j'A' Q = j'A' Q = j' A', where A' is the area of the top (or bottom) portion of the member's cross-section, above (or below) the section plane where t is measured and y' is the distance from the neutral axis to the centroid of A'. or A'= Area of the section above/below t. j' = Distance of the centroid of A' to Neutral Axis (N.A.) 4r E(А) (Location of Neutral Axis) = y = ΣΑ (I about the Neutral Axis) I = Iy'+ Ad,?
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