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Mock Exam for Finite Element Analysis, Exams of Elements of Engineering Systems

University of Texas - Tyler Elements of Engineering Systems

Summary for Exam 1 in Finite Element Analysis

Typology: Exams

2019/2020

Uploaded on 03/02/2024

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Mock Exam FEA

A shaft is made of three parts, as shown in the accompanying figure. Parts AB and CD are made

of the same material with a modulus of rigidity of G=9.8×103ks, and each has a diameter of

1.5 in. Segment BC is made of a material with a modulus of rigidity of G=11.2×103ksi and has

a diameter of 1 in. The shaft is fixed at both ends. A torque of 2400 lbin is applied at C. Using

three elements, determine the angle of twist at B and C and the torsional reactions at the

boundaries.

Partial preview of the text

Download Mock Exam for Finite Element Analysis and more Exams Elements of Engineering Systems in PDF only on Docsity!

A shaft is made of three parts, as shown in the accompanying figure. Parts AB and CD are made

of the same material with a modulus of rigidity of G=9.8×10 3 ks, and each has a diameter of

1.5 in. Segment BC is made of a material with a modulus of rigidity of G=11.2×10 3 ksi and has

a diameter of 1 in. The shaft is fixed at both ends. A torque of 2400 lb in is applied at C. Using

three elements, determine the angle of twist at B and C and the torsional reactions at the boundaries.

A 10-in slender rod weighing 6 lb is supported by a spring with a stiffness k=60lb/in.

A force P=35lb is applied to the rod at the location shown in the accompanying figure.

Determine the deflection of the spring by applying the minimum total potential energy

concept.

You are hired by an engineering firm to certify and, if needed, improve upon the initial design of a space truss. The initial design of the structure is given in figure below. The truss is made of A36 steel with 𝐸 = 200 𝐺𝑃𝑎, yield stress of 𝜎𝑦 = 250 𝑀𝑃𝑎 and density of 𝜌 = 8000 𝑘𝑔/𝑚^3. The current price of A36 steel is $0.65 per kg. The team that originally designed this bridge used a factor of safety (FS) of FS = 3 for all design purposes and they made sure that 𝐹𝑆. 𝜎 < 𝜎𝑦 𝑖𝑛 𝑎𝑙𝑙 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 … ( 1 𝑎) 𝐹𝑆. |𝜎| < 𝜋^2 𝐸 8

𝑑 𝐿

2 𝑖𝑛 𝑡ℎ𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑤𝑖𝑡ℎ 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠 … ( 1 𝑏) Where d is the diameter and L being the length of the member. In the initial design, all bars have a diameter of 8mm. Utilizing the Finite element method find out if the initial design truly satisfy conditions outlined in Equation 1a and Equation 1b? If not, clearly state which elements do not satisfy those conditions?