Question

1. If you needed to reduce deflection in a loaded aluminum rectangular box beam in your structural design, which of the following variables would you INCREASE?  Which would be the MOST effective in reducing deflection?  

                                    L               W             w              H              h

2. For question 1 above, what material could you substitute for aluminum in your design to decrease the deflection? Why?  

3.   Which has the larger Area Moment of Inertia, a 2” x 2” square beam of high strength stainless steel or a 2” x 2” square beam of balsa wood? Support your answer qualitatively or quantitatively.  

4. Should the Elastic modulus of a beam change if the unsupported length of the beam is changed?  Why?

5.    What would be the percent change in deflection if a solid rectangular beam has its unsupported length changed from 30 inches to 36 inches?   SHOW YOUR CALCULATION. What does this tell you about the importance of unsupported beam length in structural design?

6.   Is the Modulus of Elasticity indicative of what the failure load of a beam would be? Why?

7.   Which has a higher resistance to deflection (that is, a smaller ratio of Dy/P), a solid square, 1”x1” beam, or a square box beam with outer dimensions of 1”x1” and inner dimensions of 0.95”x0.95”? (Assume that L and E are the same for both.) What advantages are there to using the box beam instead of the solid beam?

Answer 1

Deflection = 5wL⁴/384EI, w is uniformly distributed load, L is unsupported length, E is Elastic modulus, I is Moment of Inertia

1. Increase H, it will increase the moment of inertia by cube times. Since deflection is inversely proportion to moment of inertia.

2. Change from aluminium to steel since steel has more elastic modulus which will reduce deflection

3. Both will have same area moment of inertia since it is dependent on section dimension and not material. Since both beam have same dimension it will have same values for area moment of inertia

4. (36⁴-30⁴)/30⁴ *100 = 107.36%, when the unsupported length increases deflection increases.

5. No, because its ratio of stress to strain within proportionality limit which is slope of stress strain curve.

6. Needs clarity on what is Dy/P, however for equal weight of section hollow section is better for deflection reduction since it has larger moment of inertia.