hw15-a beam stresses ii

Name: __________________________________________________________ CWID: ______________________________

HW15-a Beam Stresses IIYou may (1) print this file and write directly on the hard copy; or (2) annotate the PDF digitally. When done,upload the PDF to Canvas. Keep the master copy in your course binder. All expectations from LE00 are in effect.

Part I. BASICS

(1) Annotate (mark-up) the flexural stress section in your binder copyof the FE equation book. It’s on the top of page 136. Write theflexure formula at right.

Note: I usually don’t teach s (the elastic section modulus) in thisclass. Civil majors will learn all about s in upper-level classes.

(2) The flexure formula tells us that the flexural stress is a function ofinternal bending moment. The bigger the moment, the bigger thestress.

You want to know the maximum flexural stress in plane a-a. Whatis the fastest way to compute the internal bending moment at thatplane: cut a section through a-a or shear and moment diagrams?

Now, you want to know the maximum flexural stress that occursanywhere along the length of the member. What is fastest: themethod of sections or shear and moment diagrams?

(3) This beam has been cut at plane a-a so that we can visualize theinternal shear (V) and moment (M). The direction of M is correct asdepicted, and the magnitude is 240 kip-inches. Compute theflexural stress at Point A. Report your answer with a (T) if Point Aexperiences tension, and with a (C) if it experiences compression.

(4) Here, the same beam has been oriented “flatwise.” The direction ofM is correct as depicted and the magnitude is 240 kip-inches.Compute the flexural stress at Point B, reporting your answer witha (T) or a (C).

HW15-a Beam Stresses II | copyright Prof. Susan Reynolds 2021 | [email protected] | page 1 of 4

(5) Briefly reflect on the last two answers (youshould have calculated magnitudes of 2.4 ksiand 4.0 ksi). What do those problems teachyou about strong-axis vs. weak-axis bending?

(6) The curly arrow we use for moment (↺ or ↻)is great for 2D drawings but is ambiguous in3D. In 3D, we prefer double-arrow notation.These two FBDs mean the same thing. Pointyour right thumb to match the direction ofthe double-arrow. The curl of your fingersdefines the direction of the moment. Be sureyou are visualizing the way the I-shapedcross-section rotates about the x-axis.

Compute the stress at Points A and B.Illustrate them on stress cubes.

Given: |M| = 135 k-ft; Ix = 283.3 in4

(7) This beam is bent about its centroidal x-axis. It is made of a materialthat fails in two ways. It crushes in compression at 5.0 ksi. It alsoruptures in tension at 5.0 ksi. Based on these stresses, what (magnitudeof) bending moment fails the beam? Given: Ix = 250 in4 Ans. 19.8 k-ft.

(8) Rework the same problem. This time, say that the beam is being bent about the centroidal y-axis. Whatmoment fails the beam? Given: Iy = 67.5 in4 Ans. 9.38 k-ft.

(9) Briefly reflect on the last two problems. What did they teach you about strong-axis vs. weak-axis bending?

HW15-a Beam Stresses II | CEEN 311 | copyright Prof. Susan Reynolds 2021 | [email protected] | page 2 of 4

Part II. PROBLEM-SOLVING

(10) At right, I have written the flexure formulatwice. Students are often confused by all of thex/y/z references in the equations.

Draw a FBD of the bent phone linked below.Please draw in 2D. Draw the axes so we cancheck them. Make sure that your axes matchthe equations above.

https://cdn.cultofmac.com/wp-content/uploads/2014/09/iphone6bendtest.gif

If you are confused about any of the x/y/zreferences in the equations, please write yourquestions here so we can help!🌶🌶

(11) What is the significance of the minus sign in the flexure formula? Circle the correct terms.🌶

If there is a POSITIVE internal bending moment on a plane, then the flexural stress (at a point)is positive (meaning [tensile] | [compressive] ) for [positive] | [negative] values of y.In other words, tensile stresses are present [above] | [below] the neutral axis.

If there is a NEGATIVE internal bending moment on a plane, then the flexural stress (at a point)is positive (meaning [tensile] | [compressive] ) for [positive] | [negative] values of y.In other words, tensile stresses are present [above] | [below] the neutral axis.

(12) The moment diagram for this beam is provided.The beam is a square in cross-section.🌶

If asked to solve for the maximum flexuralstress, what moment would you plug into theflexure formula?

Is Point C in tension or compression?

Is Point D in tension or compression?

(13) Snow has accumulated on the branch of adeciduous tree, as shown. The weight ofthe snow will fail the branch when theactual flexural stress exceeds the stresslimits of the living wood fibers.

Worried about the tree, you are thinkingabout knocking off the snow. You decide todo some calculations first. You model thetree branch as a circular cross-section andthe snow as a triangular load.

What is the maximum flexural stress?🌶




(14) A T-shaped cantilever beam supports apartial uniformly distributed load (a lineload). You are interested in theworst-case (maximum) flexural stresses.Your objective is to construct thedistribution of stress at that worst-caseplane.🌶🌶

You will have to do ALL of the steps(centroid, moment of inertia, shear andmoment diagrams, flexure formula), sobe sure to check your numbers as you go!

= 6.5 in.; I = 290.7 in4; Mmax = 126 k-ft𝑦Partial answer: 18.2 ksi and 33.8 ksi.


hw15-a beam stresses ii

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