6.11 Obtain the relationship between the B.M., S.F., and intensity of loading of a laterally loaded beam. A simply supported beam of span L carries a distributed load of intensity k x/L² where x is measured from one support towards the other. Find: (a) the location and magnitude of the greatest bending moment. (b) the support reactions. [0.63L, 0.0393 kL², kL/12, kL/4]

6.11 Obtain the relationship between the B.M., S.F., and intensity of loading of a laterally loaded beam. A simply supported beam of span L carries a distributed load of intensity k x/L² where x is measured from one support towards the other. Find: (a) the location and magnitude of the greatest bending moment. (b) the support reactions. [0.63L, 0.0393 kL², kL/12, kL/4]

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Determine the member end moments and reactions for the continuous beam shown in the Figure (a) due to the uniformly distributed load and due to the support settlements of 10 mm at A, 50 mm at B, 20 mm at C, and 40 mm at D. Use the three-moment equation. Ans. MB =115.2 kN.m , MC = 451.2 kN.m, Ay = 138.5 kN, By = 277.9 kN, Cy = 378.7 kN, Dy = 104.9 kN
A rectangular beam is supported at both ends. It carries two concentrated load of 110kN, a clockwise moment of 110kN-m, and a uniformly distributed load "w". The modulus of elasticity of the beam is 60GPa. Solve the following if the reaction at point B is 328.90256410256kN, upward. BEAM DIMENSION: Width = 190mm , Height = 390mm NOTE: b = 4.8m ; Determine the deflection at midspan
A simply supported beam 6 m in span is supported at A and B. The beam is carrying a uniformly distributed load of intensity 20 KN/m over the whole span. A concentrated load of 80 KN (point C) at a distance of 2 m and a clockwise moment of 50 KN-m (point D) at a distance of 4 m from the left support A respectively. Find the slopes at the supports and the deflections at points C & D. Also find the maximum deflection in the beam. EI =constant.
Three cables pull on the pipe such that they create a resultant force R. Two of the cables are subjected to known forces as shown. Assuming all forces are coplanar, determine: (a) the partial resultant P of the two known forces and (b) the minimum R if ?? = 23°. What is the corresponding magnitude of F? Also, (c) resolve the minimum R in its components in f and m axes which coincide with the lines of action of the 600 and 400-lb forces, respectively. Note that the sense of F in the figure is just assumed.
The structure of a beam with single supports is subjected to a moment MA at the pinned end A, an inclined load FB applied at point B, and a uniformly distributed load with intensity q1 on the segment BC. Find the support reactions at joints A and C, then calculate the internal forces at the midpoint of BC. MA= 380 N.m FB = 200 N q1= 160N/m a= 3 m b= 2m
A 10-meter-long simply supported beam is carrying a concentrated load of magnitude 8 kN at its midspan and a uniformly distributed load of 4 kN/m from its roller support to a point 3m from its pin support. 1. Solve for the internal shear and moment developed at the midspan due to the given loads.2. Express the internal shear and moment of the beam as function/s of x.
A 5.7-m simply supported beam supports a trapezoidal distributed load. The intensity of the load varies linearly from 0N/m at supports A to 63.91N/m at support B. A)Calculate the location of zero shear.B) Calculate the maximum moment experienced by the beam.
The T-beam shows forces acting on its cross section. It was determined that the resultant R of the two forces has a magnitude of 4 kN acting 15 degrees above the NEGATIVE yaxis. Determine the magnitude of F1 and the inclination angle of F2.
Draw the shear-force and bending-moment diagram for the beam shown. Assume the upward reaction provided by the ground to be uniformly distributed. Let a = 3.6 ft, b = 4.3 ft, P = 26 kips, and w = 2.6 kips/ft. Label all significant points on each diagram. Determine the maximum value of (a) the internal shear force and (b) the internal bending moment.Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number.
Determine the intensity w of the distributed force acting on the beam shown if the resultant force R acts vertically downward at 20 m to the right of point O.
Draw the shear-force and bending-moment diagram for the beam shown. Assume the upward reaction provided by the ground to be uniformly distributed. Let a = 5.0 ft, b = 4.5 ft, P = 21 kips, and w = 3.0 kips/ft. Label all significant points on each diagram. Determine the maximum value of (a) the internal shear force and (b) the internal bending moment. Note that answers may be positive or negative. Here, "maximum" refers to the largest magnitude value, but you should enter your shear force and bending moment with the correct sign, using the sign convention presented in Section 7.2 of the textbook. If the magnitudes of the largest positive and largest negative values are the same, enter a positive number.
An 8-meter long horizontal beam is supported to the left end by a fixed support and supported to the right end by a roller support. A uniformly varying load from 0 at the left end to 50 kN/m at the right end is applied onto the beam. Assume that the vertical reaction at the roller support is 165% of the vertical reaction at the fixed support. Calculate for the location of the maximum bending moment (in meters) from the right support. Input to the nearest two decimal places.