direct and bending stress

Subject name : structure analysis-1Subject code : 2140608Guided by :- Prof. Pritesh Rathod Prof. Rajan lad

TOPIC:- DIRECT AND BENDING STRESS

Name Enrollment Number

Gandhi Harshil R. 141100106018Deshmukh Bhavik H. 151103106002Kotila Jayveer V. 151103106008Misrty Aditya P. 151103106009Pandya Dhrumil D. 151103106010

(A). Column :-

Axial load : When load is acting along the longitudinal axis of column. It produces compressive stress in column.

Eccentric load : A load whose line of action does not coincide with the axis of a column. It produces direct and bending stress in column.

Eccentricity (e) : The horizontal distance between the longitudinal axis of column and line of action of load. In axially loaded column e = 0

Effect of Axial and Eccentric load on Column:

When short column is subjected to axial compressive force, only direct stress(σo) is produced in the column.

Direct stress = σo = P/A Eccentric load produces both direct stress (σo) and

bending stress (σb) in column.

Direct stress = σo = P/A

Bending stress = σb =M/z= .y Z =I/Y

Maximum and Minimum Stresses :-When a column is subjected to eccentric load, the

edge of column towards the eccentricity will be subjected to maximum stress (σmax) and the opposite edge will be subjected to maximum stress.Maximum Stress (σmax) Minimum Stress (σmin)σmax = direct stress + bending stress = σo + σb

= P/A + M/Z

= P/A (1+ 6e/b)

σo = direct stress, σb = bending stress, M = Moment = P . e, e = eccentricityZ = section modulus = , I = moment of Inertia, y = distance of extreme fibre from c.g. of column.

σmin = direct stress - bending stress = σo - σb

= P/A -M/Z

= P/A (1- 6e/b)

Stress distribution in Column :-Stress distribution in column as the load (P) moves

from centre of column to the edge of column as shown in fig.

Limit of eccentricity (e limit):

The maximum distance of load from the centre of column, such that if load acts within this distance there is no tension in the column. The maximum distance is called Limit of eccentricity.When load is acting within e limit,

will be compressive. (+ve)When load is acting at the point of e limit,

will be zero.When load is acting beyond e limit,

will be tensile (-ve)

(B). Dams and Retaining Wall :-Maximum and Minimum pressure at the base of Dam :

(1) Weight of Dam: Weight = cross sectional area of dam x density of dam material W = (a + b) x (H/2)x ᵟ where ᵟ = density of dam material in kN/

(2) Total water pressure on Dam: Total water pressure = Area of water pressure diagram P = x wh x h Where, w = density of water p=wh²/2 = 1000 kg/

= 10 kN/

(3) Eccentricity (e) : Total water pressure (p) acts horizontally at height from the base of dam. Total weight of dam (W) acts vertically downwards. R is the resultant of P and W. R = Resultant (R) cut the base at point K. distance JK = x = (p/w)x(h/3) distance AJ = d = AJ + JK

eccentricity = e = d

(4) Maximum and Minimum Pressure :Maximum Pressure.

= w/b(1 6e/b)

Minimum Pressure.

= w/b(1 6e/b)

Retaining Wall :A retaining wall is a structure used to retain

soil(earth). The basic difference between dam and retaining wall is that, a dam retain water and subjected to water pressure while, a retaining wall retain earth and subjected to earth pressure.

Total earth pressure :P = x

P = x () Where, = active earth pressure coefficient

= = Angle of repose of soil

Total earth pressure (P) acts at height from the bases of retaining wall.

Stability conditions for retaining wall or Dam

A retaining wall or a dam is checked for the following conditions of stability:-

No overturning two major forces acting on retaining wall/dam are:- (a) total earth/water pressure(P) (b) weight of wall/ dam(W) for no overturning resisting moment > overturning moment JB > JK

No tension at base To avoid tension in the masonary at the base, minimum stress should not be(-ve). for no tension at base eccentricity should be less than (b/6).

No sliding total frictional force at the base of wall/dam = Fmax = for no sliding = > P if factor of safety = 1.5 /P) > 1.5

No crushing at base the material of wall/dam should be safe against crushing at the base. permissible crushing stress maximum pressure at the base

Minimum width of base for no tension

(C). ChimneyChimney And Wall Subjected to Wind Pressure:

Consider a chimney or wall having plan dimension b x d and height h. Let, weight of chimney or wall Where, = w/v A = base area w = x V w = x A x h direct stress = σo w/A = σo = x h ….(i) If there is a uniform horizontal wind pressure (p) acting on a side of width b, wind force = P = p x b x h This force will induce a bending moment on the base.

This force will induce a bending moment on the base. M = P x (h/2)Bending stress caused on the base due to moment,

=M/ZThe extreme stresses on the base are, = =