Concept explainers
Find the equations for slope and deflection of the beam using direct integration method.
Answer to Problem 1P
The equation for slope is
The equation for deflection is
Explanation of Solution
Calculation:
Consider the flexural rigidity EI of the beam is constant.
Draw the free body diagram of the beam as in Figure (1).
Refer Figure (1),
Find the reaction at support B.
Find the reaction at support A.
Draw the section at x distance from support A as in Figure (2).
Refer Figure (2),
Write the equation for bending moment at x distance.
Write the equation for
Integrate Equation (1) to find the equation of the slope.
Integrate Equation (2) to find the equation of the deflection.
Find the integration constants
Apply boundary conditions in Equation (3):
At x=0 and y=0.
At x=L and y=0.
Find the equation of the slope.
Substitute
Thus, the equation of the slope is
Find the equation of the deflection.
Substitute
Thus, the equation of the deflection is
Want to see more full solutions like this?
Chapter 6 Solutions
Structural Analysis
- Q. 2 Determine the slope at the supports of the beam shown in Fig. I using the conjugate beam method. Also, determine the deflections at B. E = 29,000 ksi and I = 1,000 in.¹. 10 ft I 40 k B 10 ft 21 60 k 10 ft I Fig. 1arrow_forwardDetermine the vertical deflection at joint C of the truss shown in Fig. 7.8(a) due to a temperature drop of 15 F 8 in members AB and BC and a temperature increase of 60 F 8 in members AF, FG, GH, and EH. Use the virtual work methodarrow_forwardQ. 2 Determine the deflections at B and C for the beam shown in Fig. 2 using the moment- area method. Also, determine the slope at D. EI is constant. E = 20,000 ksi and I = 31500 in.4. 1.5 k/ft 30 k Fig. 2 A В 6 ft 4 ft- 5 ftarrow_forward
- Q-1 Use the moment-area method to determine the slope and deflection at the free end C of the overhang beam shown in Fig. 1. (EI is constant). B + Fig.1arrow_forwardQ. I Determine the slope at the supports of the beam shown in Fig. I using the moment-area method. Also, determine the deflections at B. E = 29,000 ksi and I = 1,000 in.*. 40 k 60 k Fig. 1 B 10 ft 1 10 ft 21 10 f 1arrow_forwardDetermine the horizontal and vertical components of the deflection at joint B of the truss shown in Fig. 7.7(a) by the virtual work methodarrow_forward
- Problem 7.18 Determine the horizontal deflection at joint E of the truss shown in the figure if member BC is 18mm too long and member CE is 15mm too short. Use the method of virtual work. 4 m 4 m B 3 m a = 1.2 (10 SyC FIG. P7.16, P7.18arrow_forwardQ. 3 Determine the deflections at B and C for the beam shown in Fig. 2 using the conjugate beam method. Also, determine the slope at D. El is constant. E = 20,000ksi and I = 31500 in.¹. 1.5 k/ft H -6 ft 30 k B +4ft- C -5 ft- Fig. 2arrow_forwardQ-1 Use the moment-area method to determine the slope and deflection at the free end C of the overhang beam shown in Fig.1. (El is constant). B Fig.1arrow_forward