1.	Using any method, determine the bending moment at points A and B, and the spring force at point C. 25%

2.

A 100×180 mm rectangular beam is of a material with the stress-strain characteristics shown in the figure. 25% (a). Find the largest moment for which the entire cross section remains elastic. (b). Determine the ultimate moment capacity, and draw the resulting stress distribution. (c). What is the residual stress distribution after a release of the ultimate bending moment ? (d). Show that the residual stresses are self-equilibrating.

3.	如圖所示之壹層空間構架，柱A，B之尺寸為，柱 C，D為，且，樓高，假設樓版為剛性，承受均佈載重，考慮3個自由度（兩個平移、，一個旋轉），試問 (1). 其質量矩陣[M]及勁度矩陣[K]為何？ 【5%】 (2). 若考慮地表振動也是三個方向，試推導其運動方程式。【5%】 (3). 此結構之振動週期為何？並請列出所對應之mode shape 。【10%】 (4). 假設每個振態阻尼係數均為2%，並假設地表振動只有y方向的地表加速度 ， 其PGA=0.23g，若採用Newmark 的設計反應譜，則此結構X及Y方向的max. story drift 該為何？ 【10%】

4.	Two rigid bars, each of length L, forming a straight vertical member as shown in Figure, have torsional springs of stiffness at ideal pinned joints B and C. Determine the critical vertical force and the shape of the buckled member. 【20%】

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