SSC JE Civil Engineering Formulas 2026: Free PDF + 30 Solved Questions

CivilEase / SSC JE Civil 2026

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A subject-wise civil engineering formula sheet with units, common mistakes, 30 worked questions and a practical 21-day revision plan.

48 formula cards30 original questions21-day checklistFree printable guide

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If you are revising for SSC JE Civil Engineering 2026, use this page to practise formula recall and check the assumptions before substituting numbers. Search a formula, try an original numerical question, then open its worked solution.

Prepared by CivilEase · Edition: 11 October 2026 · Educational revision resource; not affiliated with SSC.

• Formula sheet
• 30 solved questions
• 21-day plan
• Free PDF / print
• Sources

This is a selected revision guide, not a complete syllabus or a predicted question paper. All 30 questions are original CivilEase exercises. Use your full course notes and the official syllabus alongside it. The plan assumes you have studied the subjects before.

SSC JE 2026: keep the whole paper in view

The official 2026 notice gives the following standard-duration pattern for a Civil candidate. Eligible candidates may receive additional time under the notice. Check SSC for later amendments, examination dates and candidate instructions.

Official exam pattern: standard duration

Paper	Questions / marks	Time	Wrong answer
Paper I	Reasoning 50 / 50; general awareness 50 / 50; civil & structural engineering 100 / 100	2 hours	-0.25 mark
Paper II	Civil & structural engineering 100 / 300	2 hours	-1 mark

Source: SSC official 2026 notice, sections 13-14. Do not ignore reasoning and general awareness while revising the technical subjects.

SSC JE Civil Engineering formula sheet

Read each relation together with its units and conditions. Symbols are defined locally: for example, n may refer to porosity in soil mechanics, whereas Manning roughness is written as n_M.

• Mechanics
• Concrete
• Soil mechanics and geotechnical engineering
• Fluid mechanics and hydraulics
• Hydrology and irrigation engineering
• Surveying
• Environmental engineering
• Transportation

Mechanics, strength of materials and structures

01

Direct stress and strain

$$\sigma =\frac{P}{A}$$$$\epsilon =\frac{\delta }{L}$$$$\sigma =E\epsilon$$

P = axial force; A = area; delta = change in length; L = original length; E = Young's modulus.

Use carefully: Use Hooke's law only in the linear-elastic range. 1 N/mm² = 1 MPa.

02

Poisson's ratio and elastic constants

$$\nu =-\frac{{\epsilon }_{\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{l}}}{{\epsilon }_{\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{a}\mathrm{l}}}$$$$E=2G(1+\nu )=3K(1-2\nu )$$

nu = Poisson's ratio; G = shear modulus; K = bulk modulus.

Use carefully: These modulus relations assume an isotropic linear-elastic material. Keep the minus sign when strains are signed.

03

Axial elongation and free thermal expansion

$$\delta =\frac{PL}{AE}$$$${\delta }_T=\alpha L\Delta T$$

alpha = thermal expansion coefficient; Delta T = temperature change.

Use carefully: PL/AE assumes a prismatic member with constant force and E. The thermal expression is for free expansion, not a restrained bar.

04

Elastic bending and rectangular section

$$|{\sigma }_b|=\frac{|M|y}{I}=\frac{|M|}{Z}$$$$I=\frac{b{h}^3}{12}$$$$Z=\frac{b{h}^2}{6}$$

M = bending moment; y = distance from neutral axis; I = second moment of area; Z = section modulus.

Use carefully: b and h are rectangle width and depth, with h in the bending direction. Use elastic beam theory and consistent moment units.

05

Simply supported beam under full-span UDL

$$M_{max}=\frac{w{L}^2}{8}$$$${\delta }_{max}=\frac{5w{L}^4}{384EI}$$

w = load per unit length; L = span; EI = constant flexural rigidity.

Use carefully: Both maxima occur at midspan. This is a full-span uniformly distributed load with simple supports and small deflection.

06

Euler buckling

$$P_{\mathrm{c}\mathrm{r}}=\frac{{\pi }^{2}EI}{L_e^2}$$$$L_e=k_{L}L$$

Le = effective buckling length; ideal kL: pinned-pinned 1, fixed-free 2, fixed-fixed 0.5, fixed-pinned about 0.699.

Use carefully: Use the weakest bending axis for an ideal slender elastic column. These ideal restraint factors are not a full code design check.

Further reading: MECH.

Concrete, reinforcement and steel quantities

07

Concrete elastic modulus

$$E_c=5000\sqrt{f_{ck}}$$

Ec and characteristic cube strength fck are in N/mm² (MPa). Example: M25 gives Ec = 25,000 MPa.

Use carefully: IS 456:2000 educational relation, clause 6.2.3.1. It estimates short-term static modulus, not an exact measured value.

08

Concrete flexural tensile strength

$$f_{cr}=0.7\sqrt{f_{ck}}$$

fcr = estimated flexural tensile strength; fck is in MPa and the result is in MPa.

Use carefully: IS 456:2000, clause 6.2.2. Do not confuse this estimate with direct tensile strength or characteristic compressive strength.

09

Target mean strength: supplied standard deviation

$$f_{\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{t}}=f_{ck}+1.65s$$

s = standard deviation in MPa, supplied or established for the concrete production process.

Use carefully: This is the statistical expression for the stated exercise. A full mix design must also check the applicable IS 10262 provisions; do not treat this as the only current requirement.

10

Singly reinforced rectangular section

$$x_u=\frac{0.87f_y{A}_{st}}{0.36f_{ck}b}$$$$M_u=0.87f_y{A}_{st}(d-0.42x_u)$$

fy = steel yield strength; Ast = tension steel area; b = width; d = effective depth.

Use carefully: IS 456 rectangular stress-block assumptions. The steel-yielding expression requires xu not greater than xu,max. With mm and MPa, Mu is N mm.

11

Development length

$$L_d=\frac{\varphi {\sigma }_s}{4{\tau }_{bd}}$$

phi = bar diameter; sigma s = design stress in the bar; tau bd = design bond stress appropriate to the bar and concrete.

Use carefully: IS 456:2000, clause 26.2.1. Use consistent units and applicable bond-stress adjustments; sigma s is not automatically fy.

12

Round reinforcing-bar area and mass

$$A_{\mathrm{b}\mathrm{a}\mathrm{r}}=\frac{\pi {\varphi }^2}{4}$$$$m\simeq \frac{{\varphi }^2}{162}\mathrm{k}\mathrm{g}/\mathrm{m}$$

Use phi in mm. Area is then mm². Approximate mass follows from steel density near 7850 kg/m³.

Use carefully: This is a quantity estimate. Add actual lengths, laps, hooks and bends separately; do not apply an arbitrary universal wastage rate.

Code reference: IS 456:2000, clauses 6.2.2, 6.2.3.1, 26.2.1 and rectangular-section stress-block provisions. Consult the applicable code and amendments for design; code tables are not reproduced here.

Soil mechanics and geotechnical engineering

13

Void ratio and porosity

$$e=\frac{V_v}{V_s}$$$$n=\frac{V_v}{V}$$$$n=\frac{e}{1+e}$$$$e=\frac{n}{1-n}$$

Vv = void volume; Vs = solid volume; V = total volume.

Use carefully: Enter porosity as a fraction in these relations: 40% means n = 0.40, not 40.

14

Water content and degree of saturation

$$w=\frac{M_w}{M_s}$$$$S_r=\frac{V_w}{V_v}$$$$S_{r}e=w{G}_s$$

Mw = water mass; Ms = dry solid mass; Gs = specific gravity of solids relative to water.

Use carefully: w and Sr must be fractions. For saturated soil Sr = 1, so e = wGs.

15

Dry and bulk unit weights

$${\gamma }_d=\frac{G_s{\gamma }_w}{1+e}$$$$\gamma ={\gamma }_d(1+w)$$

gamma d = dry unit weight; gamma = bulk unit weight; gamma w = water unit weight, about 9.81 kN/m³.

Use carefully: Unit weight is force per volume. Do not substitute mass density without a matching conversion.

16

Effective stress

$${\sigma }^{\prime }=\sigma -u$$

sigma = total normal stress; u = pore-water pressure; sigma prime = effective normal stress.

Use carefully: This standard relation applies to saturated soil. Positive pore pressure reduces effective stress.

17

Darcy's law

$$Q=kiA$$$$i=\frac{\Delta h}{L}$$

k = hydraulic conductivity; i = hydraulic gradient; A = total cross-sectional flow area.

Use carefully: Use laminar saturated flow. With k in m/s and A in m², Q is m³/s. Q/A is Darcy velocity, not seepage velocity.

18

Rankine active earth pressure

$$K_a=\frac{1-\sin {\varphi }^{\prime }}{1+\sin {\varphi }^{\prime }}$$$$P_a=\frac{1}{2}{K}_a\gamma H^2$$

phi prime = effective friction angle; H = retained height; Pa = active force per unit wall length.

Use carefully: Dry cohesionless soil, level backfill, smooth vertical wall, no surcharge or water, and sufficient wall movement to mobilize active conditions.

Further reading: SOIL, DARCY, RANKINE.

Fluid mechanics and hydraulics

19

Hydrostatic pressure

$$p=\rho gh$$

rho = liquid mass density; g = gravitational acceleration; h = vertical depth below a free surface.

Use carefully: This is gauge pressure for a free surface at atmospheric pressure. With SI units, p is Pa.

20

Continuity

$$Q=AV$$$$A_1{V}_1=A_2{V}_2$$

Q = discharge; A = flow area; V = mean velocity across that area.

Use carefully: The two-section equality assumes steady incompressible flow with no intervening inflow or outflow.

21

Bernoulli with pump, turbine and loss terms

$$z_1+\frac{p_1}{\rho g}+\frac{{\alpha }_1{V}_1^2}{2g}+h_p$$$$=z_2+\frac{p_2}{\rho g}+\frac{{\alpha }_2{V}_2^2}{2g}+h_t+h_L$$

z = elevation; alpha = kinetic-energy correction factor; hp = pump head; ht = turbine head; hL = head loss.

Use carefully: Steady incompressible energy balance. All terms are lengths. Set alpha approximately 1 only when the velocity profile justifies it.

22

Reynolds number

$$\mathrm{R}\mathrm{e}=\frac{\rho VD}{\mu }=\frac{VD}{{\nu }_k}$$

D = pipe diameter; mu = dynamic viscosity; nu k = kinematic viscosity.

Use carefully: Re is dimensionless. In circular pipe flow, values below about 2000 are commonly classed as laminar; transition is not an exact universal boundary.

23

Darcy-Weisbach head loss

$$h_f=f_D\frac{L}{D}\frac{V^2}{2g}$$

fD = Darcy friction factor; L = pipe length; D = diameter; V = mean pipe velocity.

Use carefully: Use the Darcy factor, not the Fanning factor: fD = 4 fF. Minor losses require separate terms.

24

Manning uniform-flow equation

$$V=\frac{1}{n_M}{R}_h^{2/3}{S}_f^{1/2}$$$$Q=AV$$

nM = Manning roughness coefficient; Rh = A / wetted perimeter; Sf = energy slope.

Use carefully: This is the SI form. For uniform flow the energy slope equals the bed slope. Do not substitute channel depth for Rh automatically.

Further reading: FLOW.

Hydrology and irrigation engineering

25

Thiessen-average rainfall

$$\overline{P}=\frac{{\sum }_i{A}_i{P}_i}{{\sum }_i{A}_i}$$

Ai = catchment area represented by gauge i; Pi = rainfall measured by that gauge.

Use carefully: The denominator is total represented area, not the sum of rainfall values. Keep all areas and all rainfall depths in consistent units.

26

Rational-method peak discharge

$$Q_p=0.278CiA$$

For this form, Qp is m³/s, i is mm/h, A is km² and C is the runoff coefficient.

Use carefully: An approximate small-catchment peak-flow method. Use an intensity tied to the time of concentration and applicable duration; it is not a runoff-volume formula.

27

Runoff depth to volume

$$V_r=1000d_{r}A$$

For this form, runoff depth dr is mm, catchment area A is km², and runoff volume Vr is m³.

Use carefully: Convert rainfall to runoff depth using the stated loss or runoff assumptions first; rainfall depth and runoff depth are not interchangeable.

28

Duty, base period and delta

$$\Delta =\frac{8.64B}{D_u}$$

Delta = irrigation depth in m; B = base period in days; Du = duty in hectares per m³/s.

Use carefully: Use duty and depth at the same location in the system. Conveyance and application losses cannot be silently ignored.

29

Application efficiency

$${\eta }_a=100\frac{W_{\mathrm{r}\mathrm{o}\mathrm{o}\mathrm{t}\mathrm{z}\mathrm{o}\mathrm{n}\mathrm{e}}}{W_{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{t}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}}\%$$

Use the same volume units for both water quantities.

Use carefully: Conveyance efficiency instead compares water delivered to the field with water diverted from the source.

30

Return period and exceedance risk

$$p=\frac{1}{T}$$$$R=1-{(1-\frac{1}{T})}^N$$

T = return period in years; N = number of years; R = chance of at least one exceedance.

Use carefully: Assumes independent years and a stationary annual exceedance probability. A 100-year event can occur in consecutive years.

Further reading: RAIN, RUNOFF, IRRIGATION.

Surveying, areas and volumes

31

Height-of-instrument levelling

$$\mathrm{H}\mathrm{I}={\mathrm{R}\mathrm{L}}_{\mathrm{k}\mathrm{n}\mathrm{o}\mathrm{w}\mathrm{n}}+\mathrm{B}\mathrm{S}$$$${\mathrm{R}\mathrm{L}}_{\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}=\mathrm{H}\mathrm{I}-\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}$$

HI = instrument height or height of collimation; RL = reduced level; BS = backsight.

Use carefully: A point's reading may be an intermediate sight or foresight. Establish a new HI after moving the instrument.

32

Levelling arithmetic check

$$\sum \mathrm{B}\mathrm{S}-\sum \mathrm{F}\mathrm{S}={\mathrm{R}\mathrm{L}}_{\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}}-{\mathrm{R}\mathrm{L}}_{\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}}$$

BS and FS sums include all instrument setups along the levelling run.

Use carefully: This checks arithmetic consistency; it does not detect every field error or prove that a benchmark is correct.

33

Trapezoidal rule for equally spaced offsets

$$A=d[\frac{O_0+O_N}{2}+{\sum }_{i=1}^{N-1}{O}_i]$$

d = common interval; Oi = offset at station i; N = number of intervals.

Use carefully: Use equally spaced offsets for this expression. Area is in m² when d and offsets are in m.

34

Simpson's one-third rule

d = common interval; N must be even, so the number of ordinates N + 1 is odd.

Use carefully: Offsets must be equally spaced. Do not force the rule onto a dataset with an odd number of intervals.

35

Simple circular curve

$$T_c=R\tan \left(\frac{{\Delta }_c}{2}\right)$$$$L_c=\frac{\pi R{\Delta }_c}{180}$$

R = curve radius; Delta c = deflection angle in degrees; Tc = tangent length; Lc = arc length.

Use carefully: This is a simple circular curve without transitions. Use degrees for the displayed arc-length expression.

36

Prismoidal volume

$$V=\frac{L}{6}(A_1+4A_m+A_2)$$

A1 and A2 = end areas; Am = actual mid-section area; L = separation of end sections.

Use carefully: Exact for a prismoid and an approximation for suitable smoothly changing sections. Am is not automatically the average of the end areas.

Further reading: NUMERICAL.

Environmental engineering

37

BOD exerted: base-e rate constant

$$Y_t=L_0(1-e^{-k_{e}t})$$

L0 = ultimate first-stage BOD; Yt = BOD exerted in time t; ke = base-e rate constant.

Use carefully: Use consistent time units. If kb is the base-10 constant, ke = 2.303kb; do not interchange the constants.

38

Hydraulic detention time

$$t_H=\frac{V}{Q}$$

V = effective tank volume; Q = volumetric flow rate.

Use carefully: If V is m³ and Q is m³/day, detention time is days. Multiply by 24 to obtain hours.

39

BOD removal efficiency

$$\eta =100\frac{S_{\mathrm{i}\mathrm{n}}-S_{\mathrm{o}\mathrm{u}\mathrm{t}}}{S_{\mathrm{i}\mathrm{n}}}\%$$

Sin and Sout = influent and effluent BOD concentrations, on the same measurement basis.

Use carefully: This concentration-based efficiency assumes comparable flow rates; for unequal flows use mass loads.

40

Population and water demand

$$Q_d=\frac{P{q}_c}{{10}^6}\mathrm{M}\mathrm{L}\mathrm{D}$$

P = population; qc = per-capita demand in litres per person per day; MLD = million litres per day.

Use carefully: This is the demand represented by the supplied qc. Apply leakage, fire demand or peak factors only when the exercise requires them.

41

Equivalent hardness

$$C_{\mathrm{a}\mathrm{s}\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{O}}_3}=C_{\mathrm{i}\mathrm{o}\mathrm{n}}\frac{50}{{\mathrm{E}\mathrm{W}}_{\mathrm{i}\mathrm{o}\mathrm{n}}}$$

Cion = contributing-ion concentration in mg/L; EWion = molecular or atomic weight divided by ionic valence.

Use carefully: Report the result as mg/L as CaCO3. Sum contributing hardness ions, not every ion in the sample.

42

Surface overflow rate

$$v_o=\frac{Q}{A_s}$$

As = plan area of the settling tank; Q = flow rate.

Use carefully: With Q in m³/day and As in m², vo is m/day. This is a hydraulic loading measure, not a complete treatment-design criterion.

Further reading: BOD.

Transportation, estimating and project planning

43

Level-road stopping sight distance: friction model

$$\mathrm{S}\mathrm{S}\mathrm{D}=0.278Vt+\frac{V^2}{254f}$$

V = speed in km/h; t = perception-reaction time in seconds; f = longitudinal friction coefficient; SSD is m.

Use carefully: A level-road educational model with constant friction. Use the values stated in the question. Grade or specified deceleration models require different braking terms.

44

Horizontal curve equilibrium

$$e_s+f_s=\frac{V^2}{127R}$$

es = superelevation as a fraction; fs = lateral friction factor; V = km/h; R = m.

Use carefully: This is the point-mass equilibrium approximation, not the separate IRC procedure for allocating superelevation or checking its limits.

45

Traffic-flow relationship

$$q=kv$$

q = vehicles per hour; k = vehicles per km; v = space-mean speed in km/h.

Use carefully: Use compatible lane and time bases. A speed averaged at one point is not automatically the required space-mean speed.

46

Time-mean and space-mean speeds

$$v_t=\frac{{\sum }_i{v}_i}{N}$$$$v_s=\frac{N}{{\sum }_i(1/v_i)}$$

vt = arithmetic mean of speeds observed at a point; vs = harmonic mean for vehicles traversing equal distances.

Use carefully: The harmonic-mean expression requires equal-distance observations. Do not average vehicle speeds arithmetically for a whole equal-distance trip.

47

Material quantity and item cost

$$V=LBT$$$$m=\rho V$$$$C=q_{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{m}}{r}_{\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}$$

L, B and T = dimensions; rho = mass density; C = cost for the measured item.

Use carefully: Match the density and volume units. Taxes, labour, transport, compaction, deductions and waste are separate assumptions, not hidden constants.

48

PERT expected activity time

$$t_e=\frac{a+4m+b}{6}$$$${\sigma }_t^2={\left(\frac{b-a}{6}\right)}^2$$

a = optimistic duration; m = most likely duration; b = pessimistic duration, in the same time unit.

Use carefully: These are classical PERT activity estimates. Project duration requires network analysis; do not add durations of parallel paths together.

Further reading: SSD.

30 original SSC JE Civil-style numerical questions

Try each question before opening the solution. Use 45 minutes for an initial diagnostic if appropriate to your level. This is a small learning set, not a full mock or evidence of exam-topic weightage.

Question 01

A steel bar carries an axial tensile load of 60 kN over an area of 300 mm². What is its direct stress?

1. 20 MPa
2. 200 MPa
3. 2000 MPa
4. 0.2 MPa

Show answer and worked solution

Answer: B. 200 MPa

Convert 60 kN to 60,000 N. Stress = 60,000 / 300 = 200 N/mm² = 200 MPa.

Common mistake: Dividing kN by mm² without converting force.

Review formula card 01

Question 02

A prismatic bar has P = 40 kN, L = 2000 mm, A = 400 mm² and E = 200,000 N/mm². Find the elastic elongation.

1. 0.1 mm
2. 10 mm
3. 1.0 mm
4. 100 mm

Show answer and worked solution

Answer: C. 1.0 mm

Elongation = (40,000 × 2000) / (400 × 200,000) = 1.0 mm.

Common mistake: Mixing a length in metres with area in mm².

Review formula card 03

Question 03

An isotropic material has E = 210 GPa and nu = 0.30. What is G?

1. 80.77 GPa
2. 105 GPa
3. 273 GPa
4. 161.54 GPa

Show answer and worked solution

Answer: A. 80.77 GPa

G = E / [2(1 + nu)] = 210 / 2.6 = 80.77 GPa.

Common mistake: Using 1 - nu instead of 1 + nu.

Review formula card 02

Question 04

A simply supported beam spans 6 m and carries a full-span UDL of 12 kN/m. Find its maximum bending moment.

1. 18 kN m
2. 36 kN m
3. 72 kN m
4. 54 kN m

Show answer and worked solution

Answer: D. 54 kN m

Mmax = wL² / 8 = 12 × 6 × 6 / 8 = 54 kN m, at midspan.

Common mistake: Using the cantilever UDL formula for a simply supported beam.

Review formula card 05

Question 05

A rectangular section is 200 mm wide and 300 mm deep in the bending direction. Find its elastic section modulus.

1. 3 × 10⁶ mm³
2. 4.5 × 10^8 mm⁴
3. 6 × 10⁶ mm³
4. 9 × 10⁶ mm³

Show answer and worked solution

Answer: A. 3 × 10⁶ mm³

Z = bh² / 6 = 200 × 300² / 6 = 3,000,000 mm³.

Common mistake: Giving second moment of area I when the question asks for Z.

Review formula card 04

Question 06

Using the stated IS 456:2000 estimate, find Ec for M25 concrete.

1. 5000 MPa
2. 125,000 MPa
3. 25,000 MPa
4. 35,000 MPa

Show answer and worked solution

Answer: C. 25,000 MPa

Ec = 5000 sqrt(25) = 5000 × 5 = 25,000 MPa.

Common mistake: Multiplying by fck instead of its square root.

Review formula card 07

Question 07

For a statistical exercise, fck = 25 MPa and standard deviation s = 4 MPa. What is fck + 1.65s?

1. 29 MPa
2. 31.6 MPa
3. 41.25 MPa
4. 21 MPa

Show answer and worked solution

Answer: B. 31.6 MPa

Target expression = 25 + 1.65 × 4 = 31.6 MPa. This arithmetic alone does not establish all mix-design requirements.

Common mistake: Presenting the statistical expression as a complete mix design.

Review formula card 09

Question 08

Estimate the mass of a straight 12 mm diameter, 10 m long reinforcing bar using φ²/162 kg/m.

1. 0.889 kg
2. 12 kg
3. 88.9 kg
4. 8.89 kg

Show answer and worked solution

Answer: D. 8.89 kg

Mass per metre = 12² / 162 = 0.8889 kg/m. For 10 m, mass = 8.89 kg.

Common mistake: Forgetting to multiply the unit mass by bar length.

Review formula card 12

Question 09

A 16 mm bar develops a design steel stress of 360 MPa. The already-adjusted design bond stress is 2.4 MPa. Find Ld.

1. 600 mm
2. 150 mm
3. 2400 mm
4. 37.5 mm

Show answer and worked solution

Answer: A. 600 mm

Ld = 16 × 360 / (4 × 2.4) = 600 mm. No further bond adjustment is applied because it is already included.

Common mistake: Applying a bar-type adjustment twice.

Review formula card 11

Question 10

A soil has void ratio e = 0.65. Find porosity.

1. 65%
2. 39.4%
3. 60.6%
4. 1.65%

Show answer and worked solution

Answer: B. 39.4%

n = e / (1 + e) = 0.65 / 1.65 = 0.3939, or about 39.4%.

Common mistake: Treating void ratio and porosity as the same quantity.

Review formula card 13

Question 11

A saturated soil has water content 24% and Gs = 2.65. Find its void ratio.

1. 6.36
2. 0.24
3. 0.636
4. 0.0906

Show answer and worked solution

Answer: C. 0.636

For saturated soil Sr = 1, so e = wGs = 0.24 × 2.65 = 0.636.

Common mistake: Entering 24 rather than 0.24.

Review formula card 14

Question 12

Total normal stress at a saturated-soil point is 180 kPa and pore-water pressure is 55 kPa. Find effective stress.

1. 235 kPa
2. 55 kPa
3. 180 kPa
4. 125 kPa

Show answer and worked solution

Answer: D. 125 kPa

Effective stress = total stress - pore pressure = 180 - 55 = 125 kPa.

Common mistake: Adding pore-water pressure.

Review formula card 16

Question 13

For a saturated laminar-flow specimen, k = 2 × 10^-5 m/s, gradient i = 0.4 and total area A = 0.02 m². Find Q.

1. 1.6 × 10^-7 m³/s
2. 1.6 × 10^-5 m³/s
3. 4 × 10^-7 m³/s
4. 8 × 10^-6 m³/s

Show answer and worked solution

Answer: A. 1.6 × 10^-7 m³/s

Q = kiA = (2 × 10^-5) × 0.4 × 0.02 = 1.6 × 10^-7 m³/s.

Common mistake: Omitting the area or confusing discharge with velocity.

Review formula card 17

Question 14

For dry level cohesionless backfill with phi prime = 30 degrees, use the ideal Rankine assumptions to find Ka.

1. 3
2. 0.5
3. 1/3
4. 1

Show answer and worked solution

Answer: C. 1/3

sin(30 degrees) = 0.5. Ka = (1 - 0.5) / (1 + 0.5) = 1/3.

Common mistake: Using the passive coefficient instead of the active coefficient.

Review formula card 18

Question 15

Steady incompressible flow is 0.12 m³/s through a pipe of flow area 0.03 m². Find mean velocity.

1. 0.004 m/s
2. 4 m/s
3. 0.25 m/s
4. 40 m/s

Show answer and worked solution

Answer: B. 4 m/s

V = Q/A = 0.12 / 0.03 = 4 m/s.

Common mistake: Multiplying discharge by area.

Review formula card 20

Question 16

For a circular pipe, V = 0.5 m/s, D = 0.05 m and kinematic viscosity = 1 × 10^-6 m²/s. Find Reynolds number.

1. 25
2. 250
3. 2500
4. 25,000

Show answer and worked solution

Answer: D. 25,000

Re = VD / nu k = 0.5 × 0.05 / (1 × 10^-6) = 25,000, dimensionless.

Common mistake: Confusing dynamic and kinematic viscosity.

Review formula card 22

Question 17

Use Darcy friction factor fD = 0.02, L = 100 m, D = 0.2 m, V = 2 m/s and g = 9.81 m/s2. Find major head loss.

1. 2.04 m
2. 0.51 m
3. 4.08 m
4. 20.4 m

Show answer and worked solution

Answer: A. 2.04 m

hf = 0.02 × (100 / 0.2) × [2² / (2 × 9.81)] = 2.039 m, or 2.04 m.

Common mistake: Using a Fanning factor in a Darcy-factor equation.

Review formula card 23

Question 18

A small catchment has C = 0.6, intensity i = 50 mm/h at the relevant duration and area A = 0.8 km². Estimate rational-method peak flow.

1. 0.667 m³/s
2. 24 m³/s
3. 6.67 m³/s
4. 66.7 m³/s

Show answer and worked solution

Answer: C. 6.67 m³/s

Qp = 0.278 × 0.6 × 50 × 0.8 = 6.672 m³/s, or 6.67 m³/s.

Common mistake: Using the km² coefficient with hectares.

Review formula card 26

Question 19

Rainfall gauges represent 2, 3 and 5 km², with rainfall depths 40, 60 and 80 mm respectively. Find Thiessen-average rainfall.

1. 60 mm
2. 66 mm
3. 11 mm
4. 660 mm

Show answer and worked solution

Answer: B. 66 mm

Weighted rainfall = (2 × 40 + 3 × 60 + 5 × 80) / (2 + 3 + 5) = 660 / 10 = 66 mm.

Common mistake: Dividing by total rainfall instead of total area.

Review formula card 25

Question 20

At the same irrigation-system location, base period B = 120 days and duty Du = 1800 ha per m³/s. Find delta.

1. 5.76 m
2. 0.0576 m
3. 15 m
4. 0.576 m

Show answer and worked solution

Answer: D. 0.576 m

Delta = 8.64 × 120 / 1800 = 0.576 m = 576 mm.

Common mistake: Reporting metres as millimetres without conversion.

Review formula card 28

Question 21

A benchmark RL is 100.000 m. Backsight is 1.250 m and a foresight to the next point is 2.100 m. Find that point's RL.

1. 99.150 m
2. 103.350 m
3. 100.850 m
4. 98.750 m

Show answer and worked solution

Answer: A. 99.150 m

HI = 100.000 + 1.250 = 101.250 m. RL = 101.250 - 2.100 = 99.150 m.

Common mistake: Adding a foresight instead of subtracting it.

Review formula card 31

Question 22

Three offsets are 2, 4 and 3 m, separated by two equal 10 m intervals. Find area by the trapezoidal rule.

1. 90 m²
2. 35 m²
3. 65 m²
4. 70 m²

Show answer and worked solution

Answer: C. 65 m²

A = 10 × [(2 + 3)/2 + 4] = 10 × 6.5 = 65 m².

Common mistake: Giving full weights to both end ordinates.

Review formula card 33

Question 23

For the same three offsets 2, 4 and 3 m at 10 m intervals, find area by Simpson's one-third rule.

1. 65 m²
2. 70 m²
3. 90 m²
4. 210 m²

Show answer and worked solution

Answer: B. 70 m²

There are two intervals, so the rule applies. A = (10 / 3) × (2 + 4 × 4 + 3) = 70 m².

Common mistake: Checking the number of offsets instead of the number of intervals.

Review formula card 34

Question 24

A tank has effective volume 500 m³ and steady flow 2000 m³/day. Find hydraulic detention time in hours.

1. 0.25 h
2. 4 h
3. 24 h
4. 6 h

Show answer and worked solution

Answer: D. 6 h

tH = 500 / 2000 = 0.25 day. In hours, tH = 0.25 × 24 = 6 h.

Common mistake: Leaving the answer in days when hours are requested.

Review formula card 38

Question 25

Influent BOD is 250 mg/L and effluent BOD is 30 mg/L at approximately equal flow. Find removal efficiency.

1. 88%
2. 12%
3. 83.3%
4. 92%

Show answer and worked solution

Answer: A. 88%

Efficiency = 100 × (250 - 30) / 250 = 88%.

Common mistake: Dividing by effluent concentration.

Review formula card 39

Question 26

Ultimate first-stage BOD L0 = 180 mg/L, base-e rate constant ke = 0.23 per day and t = 5 days. Find exerted BOD.

1. 57.0 mg/L
2. 180 mg/L
3. 123.0 mg/L
4. 167.3 mg/L

Show answer and worked solution

Answer: C. 123.0 mg/L

Y5 = 180 × [1 - exp(-0.23 × 5)] = 123.0 mg/L to one decimal place.

Common mistake: Using 10^(-kt) with a rate constant specified for base e.

Review formula card 37

Question 27

On a level road use speed V = 60 km/h, reaction time t = 2.5 s and longitudinal friction f = 0.35. Find SSD with the displayed friction model.

1. 41.7 m
2. 82.2 m
3. 40.5 m
4. 164.4 m

Show answer and worked solution

Answer: B. 82.2 m

Reaction distance = 0.278 × 60 × 2.5 = 41.7 m. Braking distance = 60² / (254 × 0.35) = 40.5 m. Total SSD = 82.2 m.

Common mistake: Calculating only the reaction distance or only the braking distance.

Review formula card 43

Question 28

Traffic density is 30 vehicles/km and space-mean speed is 50 km/h, on the same lane basis. Find flow.

1. 0.6 vehicles/h
2. 80 vehicles/h
3. 600 vehicles/h
4. 1500 vehicles/h

Show answer and worked solution

Answer: D. 1500 vehicles/h

q = kv = 30 × 50 = 1500 vehicles/h.

Common mistake: Mixing per-lane density with all-lane flow.

Review formula card 45

Question 29

Two vehicles each travel the same road-section length at 30 and 60 km/h. Find their space-mean speed.

1. 40 km/h
2. 45 km/h
3. 90 km/h
4. 30 km/h

Show answer and worked solution

Answer: A. 40 km/h

Space-mean speed = 2 / (1/30 + 1/60) = 40 km/h. Their arithmetic time-mean speed would be 45 km/h.

Common mistake: Using the arithmetic mean for equal-distance travel observations.

Review formula card 46

Question 30

A PERT activity has optimistic duration 2 days, most likely duration 5 days and pessimistic duration 8 days. Find expected duration.

1. 4 days
2. 6 days
3. 5 days
4. 15 days

Show answer and worked solution

Answer: C. 5 days

te = (2 + 4 × 5 + 8) / 6 = 30 / 6 = 5 days. Activity variance = [(8 - 2)/6]2 = 1 day².

Common mistake: Taking an unweighted sum of the three duration estimates.

Review formula card 48

A practical 21-day SSC JE Civil revision plan

Use this as a flexible revision schedule, not a promise of clearing the exam in three weeks. The subject order is an editorial choice, not a ranking of expected exam marks. Start from your weakest topics if your diagnostic suggests a different order.

Daily starting point: 4 focused hours. Allow about 120 minutes for civil revision and questions, 45 minutes for reasoning, 45 minutes for general awareness, and 30 minutes for formula recall and error-log review. Add breaks separately. On mock days, use 120 minutes for the full paper and redistribute the remaining time to review.

Day 01: Baseline and syllabus mapTake a timed diagnostic; mark weak topics against the official syllabus. Make an error log and select two trusted revision sources.

Day 02: Stress, strain and unitsRecall cards 1-3 without looking; solve axial-force exercises. Write every answer with units.

Day 03: Beams and columnsRevise bending, support conditions, UDL cases and Euler assumptions. Reattempt questions 1-5.

Day 04: Concrete properties and mix conceptsUse cards 7-9; revise cement, aggregate and concrete test concepts from your course notes.

Day 05: RCC and steel structuresUse cards 10-12; revise slabs, columns, beam limits and steel connections beyond this selected sheet.

Day 06: Soil phases and classificationUse cards 13-16; practise water-content, porosity, effective-stress and classification questions.

Day 07: Soil flow, strength and foundationsUse cards 17-18; revise shear strength, compaction, consolidation and bearing capacity from full notes.

Day 08: Fluid statics and continuityUse cards 19-21; solve pressure and energy-balance problems with clear reference levels.

Day 09: Pipe and open-channel flowUse cards 22-24; distinguish Darcy from Fanning and hydraulic radius from depth.

Day 10: Rainfall and runoffUse cards 25-27 and 30; solve weighted rainfall and peak-flow problems. Label every input unit.

Day 11: IrrigationUse cards 28-29; revise canal, dam and cross-drainage concepts from the full syllabus.

Day 12: SurveyingUse cards 31-36; revise bearings, traverses, tacheometry and instrument principles beyond these cards.

Day 13: Environmental engineeringUse cards 37-42; revise water treatment, wastewater, water-quality units and test principles.

Day 14: Transport, estimation and managementUse cards 43-48; revise road materials, rate analysis, valuation and CPM network concepts.

Day 15: First full-paper mockSit one timed Paper-I mock, including reasoning and general awareness. Review wrong, guessed and skipped answers.

Day 16: Repair the weakest two subjectsRelearn the causes of errors, then solve new problems on those concepts. Do not just memorize corrected options.

Day 17: Second mock and pacingTry a revised section order. Separate concept errors from calculation errors and time-pressure errors.

Day 18: Formula retrieval and mixed practiceAttempt all 30 CivilEase questions with solutions closed. Record first-attempt accuracy and uncertain answers.

Day 19: Third mock and targeted reviewUse a new paper or a properly timed unused practice set. Prioritize recurring errors and unfamiliar question wording.

Day 20: One-page personal error sheetReduce your notes to units, conditions and formulas you still confuse. Revise reasoning and general-awareness mistakes.

Day 21: Light recall and exam logisticsDo short recall blocks, confirm official reporting and document instructions, and protect sleep. Avoid a heavy new topic.

A diagnostic score is feedback, not a guaranteed selection predictor. Record first-attempt accuracy, time used and repeated mistakes. Reattempt wrong questions after a gap, with the answer hidden.

Free SSC JE Civil formula PDF and printable guide

Use Print / Save PDF for an immediate free copy of this page. Choose Save as PDF in your browser. The print view includes formulas, worked solutions and the plan. A compact typeset companion is available through the download button when a PDF download has been added to this post.

Free access, no account or email required. This resource is for education and revision, not project design.

Frequently asked questions

Is this the complete SSC JE Civil syllabus?

No. It is a selected revision sheet with 48 formula cards and 30 original numerical exercises. Revise the full official syllabus, including construction materials, steel design, geotechnical topics, reasoning and general awareness. The detailed syllabus is linked below.

Are these SSC previous-year questions?

No. All 30 practice questions were written for CivilEase. They demonstrate the formulas and common mistakes; they are not official SSC questions or predictions of what will appear.

Can I start this 21-day plan from zero?

It is a revision plan for learners who have already studied the subjects. If you are starting from zero, use it as a topic checklist and allow more time for full lessons and guided practice.

Can I use the formulas for real design work?

This is an educational resource. Real projects require current applicable codes, site data, verified inputs and qualified engineering judgement. A short revision formula is not a complete design procedure.

Which units should I use?

Follow the units printed on each card. Some coefficients are unit-specific: 0.278CiA uses intensity in mm/h and area in km²; 8.64B/Du gives irrigation depth in metres. Convert percentages to fractions when a relation requires them.

Sources, code references and scope

The explanations and numerical questions were written for CivilEase. Standard relations are presented with their conditions; the selected public teaching references below support the indicated concepts. No official exam question paper, coaching handout or code table is reproduced.

1. Staff Selection Commission: Junior Engineer Examination 2026 noticeSections 13 and 14: exam pattern and indicative syllabus. Check SSC for later amendments and date notices.
2. MIT OpenCourseWare: Engineering Mechanics I, Lecture 24Elasticity, signed Poisson relation and elastic beam bending.
3. NPTEL IIT Guwahati: Phase Relations of SoilsUse the successive pages for the three-phase system and its definitions.
4. NPTEL: Movement of Groundwater, Darcy's LawFlow through saturated porous media and hydraulic-gradient conventions.
5. NPTEL IISc: Advanced Foundation Engineering, Earth PressureRankine active pressure, its soil/wall assumptions and the resultant force.
6. NPTEL IIT Madras: Hydraulics, uniform-flow formula developmentReynolds number, Darcy-Weisbach factor convention and Manning context.
7. NPTEL: Engineering Hydrology, rainfall spatial averagingThiessen polygon weights are gauge-representative area divided by total area.
8. NPTEL: Hydrologic Analysis, Rational MethodAssumptions, time-of-concentration context and small-catchment limitations.
9. NPTEL IIT Kharagpur: Water requirements and dutyDuty, base period and crop-water requirement definitions.
10. NPTEL IIT Kharagpur: Water Quality and Estimation of Organic ContentFirst-stage BOD model and conversion between base-e and base-10 rate constants.
11. Federal Highway Administration: The 2001 Green Book changesExplains the older friction SSD form and the move to a deceleration-based form; use the model stated in an exercise.
12. NPTEL: Numerical integration, trapezoidal and Simpson rulesNumerical-rule context; the displayed survey forms use equally spaced offsets.

Concrete code references: IS 456:2000 (Plain and Reinforced Concrete - Code of Practice); mix-design requirements must be checked against the applicable IS 10262 edition and amendments. Educational formulas are not substitutes for a full code-based check.

Apply the ideas to civil engineering work

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Spotted an error or an unclear assumption? Mention the formula-card or question number in the comments so it can be checked.