Assignment 4

ENGR 323 Spring 2021 Group Project 4 (Due on April 13 2021)

Statically Indeterminate Frame

Problem: for the simple frame below subjected to a horizontal for P=40 kip, assume same young’s modulus E for both beam and columns, and story height is 30 ft, and bay width is 30 ft. Also assume that the column has section modulus of Ic and the beam has section modulus Ib=β Ic, where β is the ratio between the section modulus of the beam and the column, and has the value between 0.25 and 0.85.

Part a: use the force method to solve the reaction forces at A and B. (Note the reaction forces should be expressed as functions of β) (30%) Part b: based on your calculation from Part a, plot the variation of horizontal reaction force Ax with respect to β (15%); comment on why the reaction force Ax will change when the value of β changes (10%). Part c: for the case of W24x84 for the beam and W14x211 for the column, what is the value of β in this case? Calculate the reaction forces based on your derivation in part a and develop the moment diagram of the frame (5%); and use the virtual work method to calculate the horizontal displacement of C (15%) Part d: use SAP2000 to solve frame moment diagram and horizontal displacement of C for part c and compare with that from Part c; comment on possible difference (10%) Part e: what value should we take for β to reduce the reaction force Ax by 15% when compared with that from Part c? (15%) Project Report Requirements: 1) Print your results clearly! Electronic copy of your report should be submitted through iLearn before 5pm of due date. 2) Project report must have the signatures of all group members! Otherwise, it will be declined. 3) The comparison should be presented in a tabulated way. 4) Prints from SAP2000 should be clear and clean.