A beam fixed at both ends, as shown in the Fig, has a F=20 kN concentrated load applied at the centre of the span. The beam structure is supported from the bottom, by a linear spring, with k=400 N/cm. In addition, the beam structure is a attached to the adjacent vertical walls through two truss elements, with cross-sectional area of A= 11.55 x10-3 cm². Calculate the lateral (vertical) deflection and slope at the middle (Note: Iz is the same as ). Take E= 20x106 N/cm?, for all elements, and I= 2500 cm4 1 2 3 4 12 EI 6 ΕΙ. 12 ΕΙ 6El , L 6 ΕΙ. L 6 EI L' 12 El L? 2Εl. 300 30° 4Εl. (1) E500 cm- (2) 500 cm [k] = L. 6EI 12 EI 6EI 3 L 6 EI L² 2 EI L 6EI L? 4 EI 4 L

A beam fixed at both ends, as shown in the Fig, has a F=20 kN concentrated load applied at the centre of the span. The beam structure is supported from the bottom, by a linear spring, with k=400 N/cm. In addition, the beam structure is a attached to the adjacent vertical walls through two truss elements, with cross-sectional area of A= 11.55 x10-3 cm². Calculate the lateral (vertical) deflection and slope at the middle (Note: Iz is the same as ). Take E= 20x106 N/cm?, for all elements, and I= 2500 cm4 1 2 3 4 12 EI 6 ΕΙ. 12 ΕΙ 6El , L 6 ΕΙ. L 6 EI L' 12 El L? 2Εl. 300 30° 4Εl. (1) E500 cm- (2) 500 cm [k] = L. 6EI 12 EI 6EI 3 L 6 EI L² 2 EI L 6EI L? 4 EI 4 L

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

EXAMPLE 4.2 The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm²; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm?. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. %3D 0.4 m 0.3 m 30 kN D E -0.4 m 0.2 m
The steel truss shown carries a downward vertical load of 14 kN at joint B. The diagonal members of the truss have an area equivalent to 250 mm^2, and the horizontal members are 300 mm^2. With the given conditions calculate the: a) Horizontal Deflection at E in mm b) Vertical Deflection at D in mm Esteel = 200 GPa
Prob 5. Calculate the maximum deflection dmax and the angle of deflection on the supports of a uniformly loaded simple beam loaded as shown. The maximum bending stress is o=60 MPa. The cross section of the beam is square with a length of 8 cm on each side. The beam is made of aluminum having modulus of elasticity E = 70 GPa. q = 2.0 kN/m L= 2.0 m
The steel truss with E=200GPais loaded as shown in the figure. Determine the following: the following a) the deformation of member AB if the cross-sectional area is 2500mmb) the deformation of member AD if the cross-sectional area is 1800mm A 4.0m 200 KN B D 4.0m 1² 2.5m
A steel strut S serving as a brace for a boat hoist transmits a compressive force P= 57 kN to the deck of a pier as shown in the figure. The strut has a hollow square cross section with wall thickness t = 9 mm and the angle O between the strut and the horizontal is 30°. A pin through the strut transmits the compressive force from the strut to two gussets G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck. The diameter of the pin is dpin = 16 mm, the thickness of the gussets is tG = 14 mm, the thickness of the base plate is tg = 10 mm, and the diameter of the anchor bolts is dpolt = 10 mm. Determine the bearing stress between the anchor bolts and the base plate in MPa. ROUND OFF TO TWO DECIMAL PLACES. Pin S 16 (a) (b)
%3D QUESTION 2. An oblique bending moment of M = 5 kN.m is applied on the cross-section of an aluminum beam as shown in the figure. (a) Calculate the maximum values of compressive and tensile normal stresses on the crss section. (b) Define the orientation of the neutral axis and draw on the cross-sectionç. M = 5 kN.m 30° 10 mm 40 mm 10 mm A-40 mm--r: 30 mm 30 mm 10 mm 10 mm
A planar truss tower structure is shown in the figure. P. Externally determinate Q. External static indeterminacy = 1 R. External static indeterminacy = 2 S. Internally determinate T. Internal static indeterminacy =1 U. Internal static indeterminacy = 2 Which one of the following options is correct? (A) P-False, Q-True; R-False; S-False; T-False; U-True (B) P-False, Q-True; R-False; S-False; T-True; U-False Consider the following statements aboout (C) P-False, Q-False; R-True; S-False; T-False; U-True the external and internal determinacies of the truss. (D)P-True, Q-True; R-False; S-True; T- False; U-True
An axial member consisting of two polymer bars is supported at C as shown. Bar (1) has a cross-sectional area of 680 mm² and an elastic modulus of 29 GPa. Bar (2) has a cross-sectional area of 1580 mm² and an elastic modulus of 15.2 GPa. Determine the deflection of point A relative to support C. 70 KN 0.85 m O -1.902 mm O-2.101 mm O -2.250 mm O-1.354 mm O -2.879 mm 90 kN (1) 90 kN B (2) 1.15 m
A steel strut S serving as a brace for a boat hoist transmits a compressive force P = 57 kN to the deck of a pier as shown in the figure. The strut has a hollow square cross section with wall thickness t = 9 mm and the angle θ between the strut and the horizontal is 51°. A pin through the strut transmits the compressive force from the strut to two gussets G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck. The diameter of the pin is dpin = 15 mm, the thickness of the gussets is tG = 12 mm, the thickness of the base plate is tB = 10 mm, and the diameter of the anchor bolts is dbolt = 12 mm. Determine the bearing stress between the anchor bolts and the base plate in MPa.
Situation 3: The rigid bar ABC has a weight of 2 kN (acting on the mid-span) shown in Figure, is hinged at A and supported by a steel rod at B, and it carries a load of 20 kN at C. 1.0 m steel L = 1.5 m A = 300 mm² E = 200 GPa -1.5 m- 20 kN 7. Determine the axial stress in the steel rod 8. What will be the vertical deflection at point C 9. What will be the vertical deflection at point C if the temperature in steel rod is increased by 30°C (a = 11.7 x 106/°C)
For the truss in figure below, the cross-sectional area of the truss members is A=500 mm² and Young's modulus E= 200 GPa. Let P = 93.7 kN. 1 m √3 m B Ø D 1 m √3 m F Determine: a) Strain energy for truss AC. Enter your answer in Jto 2 decimal places. b) Strain energy for truss AB. Enter your answer in J to 2 decimal places. c) Strain energy for truss BC. Enter your answer in J to 2 decimal places. d) Strain energy for truss BD. Enter your answer in J to 2 decimal places. e) Strain energy for truss DC. Enter your answer in J to 2 decimal places. f) Strain energy for truss DF. Enter your answer in J to 2 decimal places. g) Strain energy for truss FC. Enter your answer in J to 2 decimal places. h) Strain energy for truss CE. Enter your answer in Jto 2 decimal places. i) The displacement at point A. Enter your answer in mm to 2 decimal places. A
Situation 3: The rigid bar ABC has a weight of 2 kN (acting on the mid-span) shown in Figure, is hinged at A and supported by a steel rod at B, and it carries a load of 20 kN at C. 1.0 m steel L = 1.5 m A = 300 mm² E = 200 GPa -1.5 m- 20 KN 7. Determine the axial stress in the steel rod 8. What will be the vertical deflection at point C 9. What will be the vertical deflection at point C if the temperature in steel rod is increased by 30°C (α = 11.7 x 10-6/°C)