STATICS & MECHC OF MATERIALS 2
STATICS & MECHC OF MATERIALS 2 ENGR 0145
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This 14 page Class Notes was uploaded by Shanel Lubowitz on Monday October 26, 2015. The Class Notes belongs to ENGR 0145 at University of Pittsburgh taught by Staff in Fall. Since its upload, it has received 217 views. For similar materials see /class/229412/engr-0145-university-of-pittsburgh in Engineering and Tech at University of Pittsburgh.
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Date Created: 10/26/15
Flexure of Beams Design of Beams for ENGR0145 Learnlng Objectives Flexure of Beams Des1gn of Beams for B mmmm m Strength PM ENGR0145 Statics and Mechanics of Materials 2 5 William S Slaughter Mechanical Engineering Depaltment University of Pittsburgh Student Learning Objectives Students should be able to gt select the lightest beam of a given type for a particular application7 such that the allowable exural and shearing stresses are not exceeded Flexure of Beams Design of Beams for ENGROMS Learning Objectives Design for sprengpn g Design Criteria Flexure ofBeams Design of Beams for Recall ENGROMS M c M VQ am I 7 S and 77 For a particular beam application ie7 longitudinal dimensions7 method of support7 and external loads and given an allowable exural stress can and shearing stress Tall dictated by the material7 eg7 structural steel7 how does one choose an appropriate ie7 the lightest beam of a particular type Flexure of Beams Steps in the Design Process Desigmeem for Strength ENGR0145 7 Mo 7 M d 7 VQ Tina T i g an 7 i It Learning Objectives Design for Strength 1 Determine the maximum using the bending 353127 6 moment diagram gt Given Jan gt Choose the lightest beam such that S gt Smirk gt Note that the lightest acceptable beam is not necessarily the beam with the smallest section modulus 2 After including the weight of the beam as a uniformly distributed load7 determine the new7 larger max gt Determine the new 3min maxJan gt Check that S gt 5min stilll gt If S lt 5mm pick a new beam and start over Steps in the Design Process M c M VQ 7 7 and 7 Um I S T It 3 Including the weight of the beam7 determine the maximum lVl using the shear force diagram gt Given Tall Check that Tmax lt Tani gt If Tmax gt Tall pick a new beam and start over Note most of the time but not always7 step 1 will give you the right beam Steps 2 85 3 will just be checks that will not require you to change your original choice of beam Exceptions usually are due to relatively low allowable shear stress Flexure of Beams Design of Beams for ENGROMS Example 22kN 40kN 22kN l15ml l l 125m 125m 15m For a beam made of structural steel 0811 152 MPa and Tall 100 MPa7 select the lightest American Standard Beam see Table A 4 for the loading shown Flexure of Beams Design of Beams for ENGROMS Flexure of Beams Example Design Qf Beams for Strength ENDED 145 V kN Example Step 1 determine the minimum allowable section modulus7 neglecting the weight of the beam Mmax 825 kNm Mmax 0511 7 825 x 103 Nm 152 x 106 Nm2 3 543 x 104 m3 x 103 E m gt 5min 543 x 105 mm3 543 x 103 mm3 gt Try an S305gtlt47 beam gt 5330M 596 X 103 mm3 39 73305x47 47 kgm Flexure of Beams Design of Beams for ENGROMS Flexure of Beams Example Design 6 Beam for Strength Step 2 determine the new minimum allowable section ENGROMS modulus7 including the weight of the beam w 47 kgm981ms2 461 Nm Rjeight Rgeight 461 Nm55 m 1268 N Learning Objec ves f0 S r39eh39 ph R a V N 1268 1743 Nrm 275 55 x In 71268 might 1268 N Ml fjjifht 1743 N m Flexure of Beams Design of Beams for Example ENGR0145 MW 3 MES M n izixght Eli50 g 825 gtlt 103 Nm 1743 NIH 5448914 g 842 x 103 Nm Mmax 711 lt 842 x 103 Nm 152 x 106 Nm2 g 554 X1074 m3 g 554 x 103 111mg EX gt Slum 3305X47 596 x 103 mmg still okay Flexure of Beams Example Design of Beams for Strength Step 3 check the shearing stress7 including the weight ENGROMS of the beam Learning ObJSQtweS m r S Vm V333 might 42 x 103 N 1268 N g 433 x 103 N Flexure of Beams Example Design of Beams for Strength Special approximation for I type beams only ENGROMS large I and small y Q gives small 1 A web 1 z VA web nearly const Q const I gives nearly const 1 V 739 z 7 max Aweb Example Web Depth Thickness i Flange lTThickness Flange Width For S305x47 beam gt Depth is 3048 mm gt Flange thickness is 138 mm gt Web thickness is 89 mm Aweb 0008903048 7 200138 2467 gtlt 103 m2 Flexure of Beams Design of Beams for ENGROMS Learning Objectives Design for Spiel 12th Example N max Tmax A Web N 433 x 103 N N 2467 x 103 m2 x 176 MPa Tan 100 MPa gt 8305 gtlt 47 is still okay Answer the lightest acceptable American Standard Beam is an 305x47 Flexure of Beams Design of Beams for ENGROMS Learnlng objecmves Dgssigxi so sgr39e ggh Pr