CE 1302 – STRUCTURAL ANALYSIS – CLASSICAL METHODS
UNIT-I DEFLECTION OF DETERMINATE STRUCTURES 1.Why is it necessary to compute deflections in structures? Computation of deflection of structures is necessary for the following reasons: a. If the deflection of a structure is more than the permissible, the structure will not look aesthetic and will cause psychological upsetting of the occupants. b. Exessive deflection may cause cracking in the materials attached to the structure. For example, if the deflection of a floor beam is excessive, the floor finishes and partition walls supported on the beam may get cracked and unserviceable. 2.What is meant by cambering technique in structures? Cambering is a technique applied on site, in which a slight upward curve is made in the structure/ beam during construction, so that it will straighten out and attain the straight shape during loading. This will considerably reduce the downward deflection that may occur at later stages. 3.Name any four methods used for computation of deflections in structures. 1. Double integration method 2. Macaulay’s method 3. Conjugate beam method 4. Moment area method 5. Method of elastic weights 6. Virtual work method- Dummy unit load method 7. Strain energy method 8. Williot Mohr diagram method 4. State the difference between strain energy method and unit load method in the determination of deflection of structures. In strain energy method, an imaginary load P is applied at the point where the deflection is desired to be determined. P is equated to zero in the final step and the deflection is obtained. In unit load method, an unit load (instead of P) is applied at the point where the deflection is desired. 5.What are the assumptions made in the unit load method? ` 1. The external & internal forces are in equilibrium. 2. Supports are rigid and no movement is possible. 3. The materials is strained well with in the elastic limit. 6.Give the equation that is used for the determination of deflection at a given point in beams and frames. Deflection at a point is given by, I = l Mx mx dx EI 0 where Mx = moment at a section X due to the applied loads mx = moment at a section X due to a unit load applied at that point I and in the direction of the desired displacement EI = flexural rigidity
7.Write down the equations for moments due to the external load for beam shown in Fig. X2 X3 X1 50KN A B x RA 5m X1 x x RB X2 X3 10m Portion AC CD DB Mx RAx RAx - 50(x-4) RAx - 50(x-4) Limits 0 to 4 4 to 5 5 to 10 8.Distinguish between pin jointed and rigidly jointed structure. Sl.no 1. Pin jointed structure The joints permit change of angle between connected member. 2. The joints are incapable of transferring any moment to the connected members and vice-versa. Rigidly jointed structure The members connected at a rigid joint will maintain the angle between them even under deformation due to loads. Members can transmit both forces and moments between themselves through the joint. 3. The pins transmit forces between connected member by developing shear. Provision of rigid joints normally increases the redundancy of the structures. 9.What is meant by thermal stresses? Thermal stresses are stresses developed in a structure/member due to change in temperature. Normally, determine structures do not develop thermal stresses. They can absorb changes in lengths and consequent displacements without developing stresses. 10. What is meant by lack of fit in a truss? One or more members in a pin jointed statically indeterminate frame may be a little shorter or longer than what is required. Such members will have to be forced in place during the assembling. These are called members having Lack of fit. Internal forces can develop in a redundant frame (without external loads) due to lack of fit. 11. Write down the two methods of determining displacements in pin jointed plane frames by the unit load concept. The methods of using unit loads to compute displacements are, i) dummy unit load method. ii) using the principle of virtual work.
12. What is the effect of temperature on the members of a statically determinate plane truss. In determinate structures temperature changes do not create any internal stresses. The changes in lengths of members may result in displacement of joints. But these would not result in internal stresses or changes in external reactions. 13. Distinguish between ‘deck type’ and ‘through type’ trusses. A deck type is truss is one in which the road is at the top chord level of the trusses. We would not see the trusses when we ride on the road way. A through type truss is one in which the road is at the bottom chord level of the trusses. When we travel on the road way, we would see the web members of the trusses on our left and right. That gives us the impression that we are going` through’ the bridge. 14. Define static indeterminacy of a structure. If the conditions of statics i.e., H=0, V=0 and M=0 alone are not sufficient to find either external reactions or internal forces in a structure, the structure is called a statically indeterminate structure. 15. Briefly outline the steps for determining the rotation at the free end of the cantilever loaded as shown in Fig. W B A l X Ans: W B A l A l a. Mx = -Wx b. mx = -1 l c. d. B = Mx mx dx EI 0 x B 1 X l = (-Wx) (-1) dx EI 0 16. The horizontal displacement of the end D of the portal frame is required. Determine the relevant equations due to the unit load at appropriate point. B 4m A 3m 30 KN 3m E C