# Activity 2.3b Engineering Problem Solving Answer Key

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1 Activity.3b Engineering roblem Solving Answer Key 1. A force of 00 lbs pushes against a rectangular plate that is 1 ft. by ft. Determine the lb lb pressure in and that the plate exerts on the ground due to this force. ft in 1. SOLUTION ress /A Area A x 1 ft convert to in 1in 1in A 1 ft 1ft 00lb lb ress 100 A ft ft Or ress 00lb 88in ft x x 88in 0.7 psi. A piece of steel wire 100 feet long, with a cross-sectional area of 0.00 sq. in., must be stretched with a pull of 1 pounds when in use. If the modulus of elasticity of steel is 30,000,000 psi:. SOLUTIONS a) What is the total elongation δ in the entire length of the wire? Knowns: A.00 in L 100 ft 100 in E 30 x 10 psi δ L AE (1lbs)(100in) (.00in )(30x in b) What tensile stress is produced by the pull? σ lbs A 1.00in 000 psi

2 3. A by rectangular piece of steel, that is 0 feet long between centers of the pins at its ends, is used as the diagonal member in a bridge. If the total tensile load in the steel is 80, 000 pounds and the modulus of elasticity is 30, 000,000 psi, calculate: 3. SOLUTIONS a) The tensile stress- Knowns: 80,000 lbs E 30 x 10 psi A x 8 in σ A 80000lbs 8in psi b) The total elongation caused by the load- L 0 x 1 0 δ L AE (80000lbs)(0in) (8in )(30x in c) The unit elongation- δ 0.080in ε in. L 0in. A sample of material is ¼ diameter and must be turned to a smaller diameter to be able to be used in a tensile machine. The target breaking point for the material is 95 pounds. The tensile strength of the material is 3,750 psi. What diameter would the sample have to be turned to in order to meet the specified requirements?. SOLUTION Knowns: 95 lbs δ 3,700 psi (at pt of failure) 1) A ) σ A ΠD Combine Equation 1 and : σ. 785D (continued next page)

3 Substitute knowns and solve for D that would just barely hold 95 lbs: 95lbs 3750 psi D 95lbs (.785in)( in D in 0.13 Therefore, part must be slightly less than Two pieces of steel are held together with six bolts. One end of the first piece of steel is welded to a beam and the second piece of steel is bolted to the first. There is a load of 5,000 pounds applied to the end of the second piece of steel. The tensile strength of steel is 7,000 psi, the shear strength is 8,000 psi. 5. SOLUTIONS a) Calculate the diameter of the bolts needed to support the load. Assume that the bolts share the load evenly: 5000lbs 9000 lbs Knowns: 9000 lbs Shear Strength τ 8000 psi (at failure) 1) τ A ) A Combine Equation 1 and : τ. 785D Substitute Values and solve for D 9000lbs 8000 psi D 9000lbs in (.785in)(8000 D.89 inch Closest standard bolt size inch

4 b) Find the width of the steel if the thickness of the steel is ¼. The bolt holes are 1/1 larger than the bolt. Section A Knowns: 5,000 lbs t.5 in D.500 in Tensile Stress σ 7,000 psi at failure Unknowns: W and Total Area shown by Section A (the area of the rectangle with the bolt hole areas removed) 1) A [W (D+1/1)]t ) σ A Combine Equations and solve for W: σ ( W D.15) t 7000 psi 7000 psi ( W ( W 5000lb (.5in).15)(.5in) 5000lb 1in.15)(.5in) 5000lb 7000 psi.5w lb.5W psi.5w in so W.0 in NOTE: If the solution to art B shown above doesn t make sense then leave some space and go to the next problem, Mr. Bayer can show you an easier way to do it in class.

5 . Determine the required nominal diameter of a threaded steel rod to carry an axial load of 1,000 pounds in tension if the tensile stress of 0,000 psi is permitted.. SOLUTION Knowns: 1,000 lbs σ 0,000 psi Unknowns: the Diameter of the steel rod: D 1) A ΠD ) σ max A Combine Equations and Solve for D: 1000 psi 0000 psi D (0000) D A piece of wire 100 feet long, with a cross-sectional area of.5 sq. in., must be stretched with a pull of 100 pounds when in use. If the modulus of elasticity of this steel is 30,000,000 psi: 7. SOLUTIONS a) What is the total elongation δ in the entire length of the wire? Knowns: 100 lbs A.5 in E 30 x 10 psi L 100 x 1 1,00 Unknowns: δ

6 Equation: L δ AE Substitute and solve: L (100lbs)(100in) δ AE (.5in )(30x b) What tensile stress is produced by the pull? 100lbs σ A psi.5in 8. A circular piece of steel, that is 0 feet long between centers of the pins at its ends, is used as the diagonal member in a bridge. If the total tensile load in the steel is 180,000 pounds and the modulus of elasticity is 30,000,000 psi, calculate: 8. SOLUTIONS a) The tensile stress- Knowns: 180,000 lbs D L 0 x 1 0 Cross sectional Area ΠD 3.1 in

7 Unknowns: σ lbs σ A 57,88 psi 3.1in b) The total elongation caused by the load- E 30 x 10 psi L (180000lbs)(0in) δ AE (3.1in )(30x c) The unit elongation- ε δ.58in L 0in A round, steel 1-1/8 diameter rod, is 85 feet inches in length, and supports an axial load () in tension. Calculate: 9. SOLUTIONS a) The maximum unit tensile stress in the rod, if the axial load () is 1,000 lb. Knowns: 1000 lbs D 1.15 L 85.5 x 1 10 Cross sectional Area ΠD 0.99 in Unknowns: σ Equation:

8 1000lbs σ A 107 psi 0.99in b) The maximum allowed load () on this rod, if the unit tensile stress must not exceed 5,000 psi. Knowns: σ max 5000 psi Unknowns: Equation: σ A Substitute and solve for : (5000 (.99 in ) 850 lbs c) The total elongation of the rod, if Ε 30,000,000 psi using the maximum allowed load from part B. L (850lbs)(10in) δ AE (.99in )(30x A sleigh is supported and held off the ground with four vertical ½ diameter rods. If the modulus of Elasticity is 10,000,000 psi and the length of each rod is 1 ft., how much weight in toys can be put into this sleigh without compressing the rods more than.01 and ultimately destroying the sleigh? 10. SOLUTION Knowns: D.5 L 1 1 E 10x10 psi

9 Unknowns: W, δ max.01 Cross sectional Area of each leg ΠD in Assume that each leg supports the load equally and that the load on each leg is : W L δ AE Substitute values and solve for :.01 in (1in) (.193in )(10x10 Solve for W: 13 lb W 5 lbs 11. A piece of wire is subjected to a load of 8000 lb. and is 0 ft. in length. The wire deforms a total of 1 in length due to this weight. If the Modulus of Elasticity is 30,000,000 psi, what is the diameter of the wire? 11. SOLUTION Knowns: 8000 lbs L 0 70 δ 1 E 30x10 psi Unknowns: D 1) A ΠD L ) δ AE

10 Combine Equations and Solve for D: 1 in (8000lbs)(70in) ( )(30x10 D (8000lbs)(70in) (.785)(30x10 D 0.9 in 1. A piece of circular aluminum with a diameter of ¼ ft. and 13 ft. in length is used as a structural component of a robot. If the tensile load applied to the component is equivalent to 8 tons and the Modulus of Elasticity is 10,000,000 psi, what is the total elongation in the entire length of the rod? 1. SOLUTION Knowns: D.5 3 L tons lbs E 10 x 10 psi Cross sectional Area A ΠD 7.09 in Unknowns: δ

11 Equation: L (18000lbs)(15in) δ AE (7.09in )(10x in 13. Calculate the stress created in a 3 diameter piece of steel that is 1 feet long between the centers of pins at its ends, and is used as a diagonal member in a bridge. The load applied to this member is 181,000 pounds and the modulus of Elasticity is 30,000,000 psi. 13. SOLUTION Knowns: lbs D 3 L 1 5 Cross sectional Area A E 30 x 10 psi ΠD 7.09 in Unknowns: σ Equation: lbs σ A 505 psi 7.09in 1. A strand of wire 1,000 ft. long with a cross-sectional area of 3.5 sq. inches must be stretched with a load of 000 lb. The modulus of Elasticity of this metal is 9,000,000 psi. What is the unit deformation of this material? 1. SOLUTION

12 Knowns: L A 3.5 in 000 lb E 9 x 10 psi Unknowns: ε L 1) δ AE ) ε L δ Solve Equation 1 for δ, then use in equation : L (000lb)(1000in) δ AE (3.5in )(9x in ε L δ.3in 1000in in. Conclusion 1. You have been asked to design a machine to punch circular holes into a sheet of metal. Create a sketch of the problem and set up the equations to calculate shear stress in the metal sheet. Make sure to include applied force, hole diameter, modulus of elasticity and sheet thickness. Students should demonstrate an understanding of the problem solving process by creating a clear sketch, with all parts labeled, and by using the correct terminology. The formulas specified should be correct for their diagram.. A community in a mountainous area has developed a playground in a park by a stream. The time it takes for children who live on the other side of the stream to walk to the playground is an hour. The stream is 0 feet across. You have been asked to come up with a design for a cable bridge for foot traffic only. What size cables will need to be obtained so 10 average-sized children can walk on the bridge at once? Some discussion should precede this problem in order to establish what an average child weighs. The answer will depend on this information and on how complicated each student wants to make the bridge design. Computer software can, and should, be used in the design process.

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